What's wrong with the old grout, exactly? Are you looking to replace all of it or just some? If it's dirty, It can be cleaned with sufficient chemicals and elbow grease. Damaged? Just remove the damaged sections and regrount where there are gaps left.
I re-grouted an entire shower in the house I have now but only because it wasn't done right originally. They didn't use enough grout, so it was either falling out (from not having enough area to hold on to) or was so thin you could poke through it with your fingernail. In this case, I didn't remove all of the grout, just enough so that I was sure the new grout would have enough to anchor to.
There are grout removal tools you can buy. The hand tools are quite a bit of work if you want to remove a lot. Otherwise, I've seen attachments and things for power tools. I remember seeing a video of a guy using one of those vibrating etcher things like a mini jackhammer. Made quick work of the old grout but also looked like it could easily chip the tile.
Applying new grout is quite easy but it sounds like you've done that before.