I’m not going to deceive you and tell you how easy it is to understand this concept because it can be easily confused with other grammar, not mention most of the grammar explanations I’ve come across regarding this point have always been piss-poor. So I can’t guarantee that this will make your understanding about this clearer, but here goes.
~てある expresses a state resulting from a purposeful action by someone (or something). This is different from ~ている which addresses the continuing state of something (in addition to expressing the progressive aspect). The key about this grammar is the resultant state that you want to bring attention to. The agent (the person who does the action) may not always be clear, however who did the action is irrelevant (with regard to this grammar) because the focus is the resulting state.
The kicker is that this grammar can be confused with ~ている, the Japanese passive, or even the Japanese past tense due to how it can be translated into English. Again, the focus is the resultant state the subject is left in, not who did the action. In many cases, this resulting state is meant to be in preparation for something in the future. I’m going to put down some sentences that will compare ~ている and ~てある.
For example: (These sentences were either created by me or something I came across in the past).
~てある
宿題をやってある --> (My) homework is finished (because I did it earlier).
窓が開いてある 。なんでだろう?–> (Somebody) opened the window (and it’s still open now). Why did they do that?
リンクをクリックして、ホームページに行く。そこには、「文プロ」と書いてあるよ。
–> Click the link and you’ll go to the homepage. You’ll see “文プロ” written on that page.
Versus ~ている
窓が開いている。なんでだろう? --> The window is open (and it’s still open now). I wonder why it’s open?
昔から、~ている形という文法がわかっているよ。–> I’ve known about the grammar for ~ている for quite a long time.
ビールが冷えているよ! --> The beer chilled (now).
So if that was clear as mud, please feel free to browse these sites to help you understand. I find that reading a variety of explanations, I’m able to get a fuller understanding of the grammar because people are bound to miss important details. Link 1: ~ている vs. ~てある, Link 2: ~てある vs. past tense, Link 3: ~ている vs. ~てある vs. passive aspect