The bearing on the underside (the side with the tt mounted cylinder with the c clip) has a retaining c clip mounted to it. Stick a small screwdriver underneath the retaining clip and pry it up.
Take this c clip off the old bearing if your new bearing did not come with one.
To put the new bearing in, you will find that the main thing holding the bearing in place is friction. This means that it's pretty hard to get a bearing back in there. I took a wood block and a dead blow mallet and knocked it back into place slowly until the retaining clip was flush with the bottom of the TT base.