I was just rounding up my own notes about this today. I'm still pretty new to the language myself, but why not share them with you anyway, no? :)
Neko desu -> It's a/the cat.
Neko ga imasu -> There is a/the cat.
Asoko ni neko ga imasu -> There goes a cat.
It gets a bit trickier when dealing with 'doko' and such. For instance, you can say either these:
Neko wa doko desu ka? -> Where is a/the cat? (in general)
Neko wa doko ni imasu ka? -> Where is the cat? (its specific location)
So, for asking about its specific whereabouts, I could ask:
Neko wa teeburu no ue ni imasu ka? -> Is the cat on the table? (its specific location)
We say,
Mark desu -> I am Mark.
Hence,
Mark wa doko desu ka? -> Where is Mark?
To simply ask where I 'am' (desu), as opposed to wanting to know at which specific location I am manifesting my physical existence (iru). But I since 'doko' denotes location anyway, asking where someone 'desu', in combination with 'doko', is inevitably, indirectly, also asking at which location that person 'is' (iru).
So, if you wanted to really inquire about my physical whereabouts, you could say:
Mark wa doko ni iru no? (Or "Doko ni iru ‘n desu ka?" and variants)
--
Arimasu (aru) indeed is used for inanimate things, like:
Hanashi ga arimasu -> We need to talk. (lit. "Talk (n) needs to exist.")
However, as the ever helpful chihiro-san already pointed out, in a Present Progressive, you'd use IRU, regardless:
Denwa de hanashite imasu. -> I’m talking on the phone.
That's simply because the Present Progressive almost always uses 'te' + ‘iru’.
Sometimes, you get 'te' + 'aru'. In one of my fav Amine, Macross Frontier, Ranka Lee sings a song with a line that goes like:
Neko no nikki ni wa, o-hirune no kaisuu ga kaite aru.
In the cat's diary, the number of its naps is written.