Well the software isn't important and I actually prefer when the client gives me something in Illustrator 'cause is easier for me to scale logos and other visual objects for retina displays and so. Just a small fact before going to the answer, Adobe has made a new software called Experience Design, it looks really great although is still on preview mode. Try downloading it and just remember that if you used Sketch and comes a time you have to move to Windows or have to work with a Windows guy you won't be able to send him your Sketch file, and maybe there will be a lot of people in the near future using Windows with the new updates Microsoft is making.
Now to the good, the software does not make you a good, bar or anything like a designer. For you to be able to be a Designer or Web designer you'll have to acquire 'good taste' and know basic rules and theory on UI, UX and Graphic Design, how to combine colours, figures, proportion and a lot more. I would advice you to read about UI/UX basics, and Web Design and managing combination of colours and fonts, then find inspiration like @Robert says (Dribble, Webdesigner, Behance, DeviantArt, etc).
After you find inspiration start doing some mockups or remakes of old sites or redesigning your website with Sketch, Photoshop, Illustrator, Experience Design or whatever software you decide to use and after that come here and show it to us and ask opinions about it, also ask your friends specially your designer friends, but not the ones that are just graphic designers and know nothing about web design.
And that's the way you start your way... and remember always look and see what others are doing and copy them but not just copy but transform their idea and upgrade it. Remember it is not bad to copy ideas neither rethinking them and making them better, it is bad if you just copy them just as they are and leave them like that claiming they are yours.