Long time since I changed one of these and it's rare, are you sure it needs replacing?
From memory, so don't quote me. Sometimes they just fall out or come out when you release the pull lever. If it does it's possible the casing is buggered, so check it. If the bearing isn't gripping the outer race surface and there's not too much clearance between them. A light coating of bearing fit will sort it, slide in the new bearing, use the pull rod as a guide and to seat the bearing and make sure the top bearing is in position before fitting the lower. Leave the pull rod in place while the bearing fit goes off. Ensure the pull rod is smooth in operation. If the damage is too much for bearing fit, it's a new casing.
If all well the casing the bearing should stay in place when the pull rod in removed. You can either tap them out (use a soft mallet) or just gently warm up the bearing housing and it should drop out. If you're quick, you should be able to insert the new one while the casing is still warm and the bearing will slip in easily, use the rod as mentioned above.