"Somewhat" usually means "a little bit" when used with an adjective:
- I'm somewhat confused by your answer (this is the same as "I'm a little confused by your answer.")
- He's somewhat arrogant.
Somehow can mean "by some means, in some way that I haven't yet figured out":
- Somehow I will get to Boston by Thursday (this means the same as "one way or another I will get to Boston by Thursday.")
- We will recover from this tragedy somehow.
It can also mean, when added to verbs of thinking or feeling, "sort of, kind of, maybe":
- Somehow I feel like you aren't fond of my friend Jane (this is the same as "I kind of feel like you aren't fond of her.")
- Somehow I think the mayor is going to reject my request.