Unless you are using a mountain bike cassette that has bunches more teeth than what you are currently using, the short answer is no. Just a bit of adjustment will do. It really has more to do with chanistay length. Switching to a chainring that is much larger (say three teeth or so) is a different story, and it is only a few more links (like one or two).

New chains come in one length, and you have to remove the excess. With a chain tool, you match the length of chain from what you have removed from your bike. Just pop off the excess.

But, I would watch a competent mechanic do this for your first time. No sense in doing something wrong and leaving you on the road.