What part can I use to get the connection This is what I have.. 


Would like to connect the long "thing" to the square base.. not sure which part will give me a angled elevation
In case you are wondering what I am trying to do.. this is what I am trying for the same exact purpose
http://www.youtube.com/watch?v=4PcL6-mjRNk
This may call for a bit of re-designing. I don't think there's a special piece for angled elevation, because you can mimic the effect with a gear.  

Use a 24- or 40-toothed gear, and attach your "arm" to it. This has the advantage that you can connect it to a servo or motor using a few more gears - I assume you want to mimic the ball-throwing device in the Youtube clip.  

You can connect the gear to your base in a number of ways, although personally I'd build the base from "normal" technic beams (e.g. the 16x1 types), If you insist on using your current base, you'll have to add a construction that you can put the axle through.