Can you learn artistic skills by yourself? How would one go about doing so over an extended period of time?

First of all you need a kind of plan, and you should prepare it by yourself, taking into account all your passions and possibilities.

It should be divided into smaller periods, and after every term you should do some work, that will demonstrate your current achievements.

Then you should research every part of your curriculum, and select some learning materials and references that can help you to achieve good results. Like:

online courses

youtube videos

books

blog posts and articles

favorite artists’ portfolios and works of the masters

take local classes and private lessons on specific topic

visit local museum, exhibition etc. or take virtual tour

watch movies and documentaries

Then carefully plan your time and deadlines for every theme, and begin learning!

The most important part is to study every day, at least for 1 hour.

If you feel stuck, try to skip current exercise and move further.

Hope this helps, good luck!