I have hired hundreds of outsourcing employees over the years.

A few tips would include:
#1 - Prove you can deliver. Someone is hiring you to help them solve a problem or grow. I cannot tell you how many times I have seen people say they can do something, but it was added to look good or what they think a perspective employer would like to hear. Show me you have done it before
#2 - Be on time. Respecting time is something A LOT of outsourcing companies and employees do not do. If you say, I will speak to you in 10 minutes, dont make in 30 minutes. Now I have come to use to this that I expect that if they say something, it may or may not happen when it comes to time. It is almost consistent for people to not be on time, so being on time would be refreshing.
#3 - Have strong references and ask existing clients for more leads. Your clients are likely talking to other business owners and they may have a similar need. Each time I have let a person go since the business took a turn and they were great. I have got them multiple job offers elsewhere. That is because I know they are great workers and proven, I just did not have a need for the skills.

I hope that helps :)

Cheers,
Mukul