Question

Strider offers to share what he knows with Frodo and give him advice. What does he ask in return?

Answer 1

I just read a summary of Chapter 10 in The Fellowship of the Ring, .

I think Strider  offered to share what he knows with Frodo and give him advice so that Frodo and his friends will accept Strider as their guide. 

His exact words to Frodo were: 
'Don't be alarmed!... I will tell you what I know, and give you some good advice — but I shall want a reward.'
'Just this: you must take me along with you, until I wish to leave you.'

Later on in their conversation, it was revealed that Strider was actually Aragorn and he was a close friend to Gandalf.