在 vs 着
There are a lot of things to consider when choosing 在 and 着 when expressing "-ing". But consider two points:
(1) 着 expresses some state, 在 expresses an action in progress.
- 他在开门。He's opening the door. (Picture the door half swung open.)
- 门开着，进来吧。The door is open, come in.
- 他在穿衣服。He's putting clothes on.
- 他穿着衣服。He's wearing clothes.
(2) If you want to say "while... -ing", it's probably good to go with 着.
- 他看着电视，电话响了。While he's watching TV, the phone rang.
- 他看着电视，吃着饭。这时，电话响了。While he was watching TV, he was eating at the same time.
- 他在看电视，所以没听见电话。He was watching TV, so he didn't hear the phone ring.
But there are a lot of subtle differences, it's better to learn 在 and 着 more closely on their own.