I know that I have to file a 1099 at the end of the year. What I am trying to find out is- What is a base percentage that I should with hold from each pay check, so that I will be able to pay what I owe...
Any help would be greatly appreciated!

There are too many variables involved in the consideration. You only need to pay tax on the net income of the 1099. You need to think about how much did you spend on making that income, do you have other income source, are you self-employed, how many dependents you have, etc. It's just not enough information to answer the percentage question.