You need to figure out your goals as a web designer. Are you looking for working with a large organization or start your own web development house? Is freelance development your thing? You must have the answers to these questions before you start the work as you do not want your efforts to be without an eventual goal.
You will need to learn the process of making websites. You should be able to use various tools that are on offer for this purpose as well as know the various coding languages that are used for making websites. This is a prerequisite as without this knowledge, it is not possible to be a web designer. Also, you can learn web development or design formally with the help of various courses that are on offer by various educational institutions.
You need to practice as you learn. This will speed up the learning process for you. Start off with making simple websites and experiment with them. As you learn more, you can try newer things in your work and try to be more creative. The more you practice the better you will get and the more skills you will acquire.
Work with a Development House
This is another important step in establishing yourself as a web designer. You will learn a lot during the job and will be a part of large projects which will benefit you in a big way. It will also help you in getting in touch with people in the industry with whom you may work at a later stage as well in an independent capacity.
Even if this is not your eventual goal, making independent projects will help you in getting better and making a large portfolio. This will reflect well on you as a professional and will help you in seeking greener pastures.