How am I able to sync an iphone with more than 1 computer?

I have been using the same computer for some time to sync my iphone & as a result this is where majority of my itunes collection is stored. I got a second computer recently and whilst messing about with it plugged my iphone in, it started to sync but then it asked me if I continued it would wipe the itunes content from my iphone “did I want to continue?” I pressed the ‘No’ button. I have now transferred over all my tunes (via memory stick) to the new computer & I now want to use this computer as my main itunes, I have tried syncing my iphone with this computer but whereas it says it’s syncing but in all reality very little appears to happen. Does anyone have a solution?