Quick short guide going the progression of Artist Idle.
Your first goal is to complete a picture. You slowly gain pixels as time passes. You can use pixels to buy tools that gather pixels faster, but you can use those pixel until you collect them. When the picture's layer is full of uncollected pixels, you can move up to the next layer. Moving to the next layer does not collect pixels if you don't have a certain upgrade. When you move up a layer or collect pixels, the amount of uncollected pixel in the layer reset, so you probably don't want to collect pixels right before moving up to the next layer. When you collect enough of a certain tool, you get a skill point, which can be spend on a mini-upgrade to help complete the picture faster. There are also abilities that increase you pixel gathering rate for a short while. You unlock more tools and abilities as you move up the layers. When the final layer is full of pixels, you can finish and get the picture.
Now that you have your first picture, you can sell it for some money and fame. For now, you can use money to buy some longer lasting upgrades.
Now your next goal is to complete and sell 2 more pictures to unlock the museum. The mini-upgrades, tools, and layers of the 1st picture are reset for each new picture, so it is kind of like doing the 1st picture again, only this time you have the upgrades you brought with money. When you sell 3 pictures, you will unlock the museum.
The Next Town
Now that you have unlocked the museum, you should make another picture and instead of selling it, put it in the museum. Having pictures in the museum allows you to passively gain fame, which increases how much money you get from selling pictures and is important to unlocking towns. Since you are now gaining fame passively, it might be worthwhile to wait a bit before selling a picture.
Your next goal is to unlock the next town, this will require a lot of money and fame. So you should fill the museum with pictures to get fame faster (you should stop at 8 pictures in the museum, the 9th slot is very expensive) and sell pictures to get money. You will probably have to move towns when you can't take more vacations to gain inspiration (you need inspiration to begin making a picture). Moving towns resets everything except fame. eventually you will have enough money and fame to unlock the next town.
The School and Naming a Successor
Unlocking a town resets everything (including fame), but you will start with a skill point to buy a mini-upgrade and you have another town to take a better vacation at.
Now that you have unlocked the 4th town (you already have 3 unlocked), you can buy a school (you may have to complete some pictures before the school tab appears). The school will cost a lot of money, but once you unlock it, it became cheaper to buy after moving towns and it is very helpful. When you buy a school, you will need to hire some students. you can assign students to hire more students, make pictures, sell pictures for money, and practice sketching (which makes student picture sell for more). You can increase the maximum amount of students you can have by perform lectures in the towns you have unlock (this will cost some students). When you move towns, the school will need to be brought again and you will need to rehire the students (honestly, once you buy the school, you shouldn't need to move towns). The school can handle all of the money making, so you can dedicate all of your pictures to being in the museum for the fame.
Your next goal is to name a successor. You need a lot of student to do that. I suggest unlocking all of the towns to have more places to perform lectures to speed up increasing the maximum amount of students you can have.
Once you have enough students, you can name a successor. Doing so resets everything back to the very beginning (towns become locked again, the school is full price), but you will have some harps and Palettes, a small boost to museum fame gathering speed, and your picture will sell for a bit more.
You can use the harp to buy a muse to provide some kind of boost, the muses will get reset. You should probably buy some permanent upgrades with the palettes too.
Your next goal is to unlock the gallery. I think it unlocks when you buy a 2nd muse, so you will need to name another successor 1 or 2 more times (Future Successors will need more students to name).
The gallery contains pictures you can make, but your pixel gathering speed is very slow, so I suggest not trying gallery pictures until you have a lot of money brought upgrades. Completing a gallery picture lets you start with some money when you move towns, allowing you to buy some upgrades on the first picture of a prestige.
This is the farthest I have gotten in the game, seems like all the tabs are unlocked, but you can expand the gallery with harps and I am not sure if there is an end to the gallery or if something special happens when you buy all of the muses (the 4th muse costs 125 harps).
There is a lot of waiting for fame to accumulate and you have to leave the game open for it to actually gather pixels.