changing needle size in mid-project

So I'm knitting my first soaker and the instructions say to change to a larger size needle. Is there a certain way I'm supposed to do this, or do I just slide the stitches over a couple at a time? That was what I was trying, but being as they're going onto a larger needle they're awfully tight and I'm afraid they'll break. I looked in my copy of Knitting For Dummies but it didn't say anything on the subject.