How can I improve my skills in web design?

1. Read design blogs and publications, visit art / design galleries, and go to museums. A person's design is influenced by the designs they surround themselves with, and if you're subconsciously channeling / filtering / replicating aspects of award winning designs, yours will become better.
2. Bear in mind that the web is just another medium for communicating visually. In many ways it borrows from the paradigms of print design, which borrows from the paradigms of fine art, and so forth. So in other words, don't limit the things you influence yourself with to only web design.
3. Along those lines, drawing (on physical paper) will equip you to tackle visual communication problems more creatively and effectively because it's more limiting than working on a computer. It's like having a single stick and a single drum to make a rhythm versus having the world's most elaborate drum set in front of you and twenty arms.
4. Find the most "frictionless" tools for you. I added this in because you mentioned designing in the browser which can be effective and in some cases save time, but you're at the mercy of what your coding abilities allow you to do. However the same can be said for tools like Photoshop or Illustrator: if you don't know how to operate smoothly in them, you may find yourself spending more time reading the manual and following tutorials than actually designing. Ultimately you want to be able to change things quickly in order to quickly experiment and see what they look like rearranged, resized, etc.
5. Think of design as problem solving and storytelling, and it will reduce the amount of "noise" you have in your design. Good design is about removing the unnecessary and adding just enough to get the points across.
6. Remember that there are always multiple designs that would work, and seek them all out. Don't get married to a single idea, especially early on.
7. Give it time. Design something, then walk away for an extended amount of time (a few hours at least). Come back with a clear head. You'll be able to see it more objectively, and will notice things about it you overlooked.
8. Find what inspires you outside of visual communication and use it to recharge while you aren't designing. I love films, video games, and music, so when I'm not working, I try to engage myself in those things. I find they inform my designs in subtle ways, and since they're creative mediums as well, there can be interesting crossovers.
9. Run your work by people who you feel are competent designers that would give constructive feedback. It doesn't mean that you have to take their advice, but having it in mind is helpful and they will notice things that you may not have. Also learn to take criticism gracefully, and find your own balance between defending your design and giving in. You don't want to be a pushover, but you don't want to be an asshole.
10. Find a mentor. Ideally this would be someone with whom you work that you work with on a daily basis. I find these relationships just naturally happen, but it goes back to number nine above where you may need to seek them out more than they seek to give you unsolicited feedback.

Disclaimer, I'm not a graphic designer.  But I've been working with them for almost 23 years .
It sounds like you already know how to code, which is good, but not necessary to be a good visual designer.  If you want to be a better web designer then you need to start with the basics:  Typography, Golden Proportions, Colour Theory, Balance, etc.  Once you understand the basics you can start to look at other designs and see what works, and what does not.  This takes TIME and PRACTICE. 

Even students graduating from Graphic Design courses aren't very good at a lot of this (in most cases).  They need mentorship and experience to get better. Often it's the little things that take a design from being "meh" to being "great".  Knowing how to address those little things intuitively takes experience.

The other challenges is working on your own projects vs working for others. You need to learn to design for others and not for yourself.  You need to view criticism as someone offering for free to help improve your future work and not as someone pulling you down.  Accept it, embrace it and learn from it.  Even bad criticism has some value, so seek it out.

As for designing in HTML vs in Photoshop.  Your tools don't matter really, but what you should do is follow a logical progression from easy to harder so that you can master the skills before you progress.

Start sketching layouts and concepts on paper.  For every design you probably want to experiment with a minimum of 50 thumbnail sketches. Explore different options.  Fill sheets and sheets of them.  At first you will think it is pointless, but it will force you to experiment and try different approaches.  Once you have a bunch, you can pick a few you like and then move to sketching out more refined versions.  Think about colours and typography.  What images to use, etc.
Once you have an idea you think works you can then move to the computer and start mocking it up in Photoshop

If you can't do great design with pencil and paper then you'll never do great design in Illustrator or Photoshop. Designing in HTML/CSS is even harder. You need to be pretty experienced before you can skip the initial design steps.

Best way to improve anything is practice.. you can develop your web design by following a particular routine in your life on daily basic -

Code everyday - Every developer will suggest you to write code on regular basis for better practice and improving your imagination skill. Imagination plays most important role in designing purpose. This will also improve your typing skill. when you write codes you will better learn it by correcting your errors. Don’t break the chain rule .

Learn basic elements of any website i.e. color , fonts , background etc - These are the things which makes any web page attractive . for example font size can impact the readability of a site . color can decide the impression that your website makes on any visitor . you can change the whole view of your website just by selecting appropriate fonts and colors. CSS is used for this purpose.

You can follow this CSS-Tricks for this.

Make responsive designs - Today a large number of users uses mobile phone and different devices to browse anything so it is very important that your website must react to the size of a user’s device. Bootstrap is widely used for this purpose.

Learn javascript - It's the only scripting language for client-side programming. Javascript can help you to do things that would be impossible with HTML and CSS alone. It is increasingly popular for server-side programming also.

Pinterest - you can get many good examples of web pages here Pinterest . There are many inspirational designs you can go for.

Focus on improving website speed - Don’t slow down your website by putting any fancy designs which doesn’t even look attractive. Try to make simple and clean designs. Simple designs often attracts users more and make them even understand your website purpose easily.

The first impression your website makes by the time it takes to land on landing page.

Use good quality images on your website - You can take an example of e-commerce website. If you are buying any dress and the image of the given dress is not clear . How will it attracts to you ? So it is always better to use good quality and even images that are related with the contents.

There are many things more. Try to follow online blogs and different inspirational designs.

Are you finding yourself stuck at certain level in web design. There are many ways one can enhance his/her skills in web design. Here I am listing down some of the habits you can implement for further enhancing your skill-set.

1. Subscribe to the top web design influencers and blogs so that you always be aware with latest news and tools of the industry. You can get many blogs with listicles of such blogs by just providing google with the query.
2. Best way to learn is by doing things which means you should always try to do things once you have learned because it not only provides you with confidence in some specific skill but also helps in remembering the concept.
3. If you do job in web design then try switching some jobs because it would provide you with more exposure and you would get a chance of working with types of professionals.
4. If you find something inspirational or out of the box on some website then do right click and inspect element for learning about how to do a thing.
5. Do not wait for opportunity to try out new things which you have recently learned instead start doing things once you have learned basics about how to do a thing.

To Read About the tools for web designers visit: 18 Web Design Tools Every Budding Entrepreneur and SMB Should Exploit

Designing a site is not sufficient; you have to put constant initiatives on it to meet the modifying trends of the industry. You cannot reject the fact that your website only gets the top position if it accepts all the latest trends and update on a timely basis. Creating your company website can be a difficult proposition.A well known Web Designing Company in Chhattisgarh gives complete web solution.

Following are some easy tips that assist you to improve your web design skills.

1.Design in shades of gray, then adds color: Unnecessary to say that a design or shade not only give a bad look to your website but also distract your clients. But,if you select a gray shade and put your graphic designs on it so it may prevent your site to get over-designed.

2.Design a polished and professional logo: Don't forget that logo is the name of your brand so always make it in a professional manner so that it stays longer on a client mind.

3.Get rid of clutter: Images, Animation must appeal to customers, but you also accept the fact that it may draw their attention from the vital part of your page. So always keep in mind that use design, but in a limit.

4.Simplify Navigation: So many clicks may be confusing your client and at the time they are not able to visit the page they want to, so they instantly leave it.

5.Make your text easy to use: Text is a significant part of your page; this is the only thing which gives your clients a reason to come back. So always keep it interesting and simple to read as well.