first you have to find the result of all forces on your object (if they apply on the same point), just sum up all your forces vectors and use this to find the acceleration. (F=ma, you divide your force vector by mass and you find acceleration, but it's a vector).
Now you need to integrate this over time. For this step, you need an accurate timer and the difference of time between your current frame and the last one (delta_time). Multiply your acceleration vector by this delta_time and add this new vector to your object velocity. Now take this freshly updated velocity vector and multiply it by delta_time. Add this vector to your object position and you get the updated object position. This is the Euler integrator which is not THAT accurate but still good for simple stuff.
I wrote an article in french about (basic) particles physics :
There's some code in the middle of the article that performs this integration, you should be able to understand it, it's C. For advanced motion, you'll have to read some docs about torque and momentum. (Chris Hecker series are a good start : http://www.d6.com/users/checker/dynamics.htm)