I'd always been nervous about replacing the push-fit bearings myself. I'd always been used to the screw-on variety, and when I bought a Specialized Crux with BB30 push-fit bearings I just left it as a job for my LBS when the dreaded creak would start up. Now that I have three bikes with this method of attachment, it's worth overcoming the fear of bashing those worn-out bearings out of the frame.
My Crux (which I haven't serviced yet) has BB30 bearings tapped directly into the 46mm shell in the frame. There are presumably a couple of large circlips wedged in the frame to define the internal location of each bearing.
My Ridley Noah has a 46mm shell, and is fitted with a pair of plastic Rotor housings that contain the bearings themselves (with 30mm internal diameter). The crankset is an FSA BB386 brand featuring a TeamZwatt power meter.
My Orro has a 42mm shell, so can only take a 24mm diameter crankset. It has a standard Ultegra crankset rolling on a Prime ceramic BB86 bottom bracket. I did run a Sram Rival crankset for a while (with a Stages power meter on the left arm), using a Sram GXP Team Pressfit Road BB86 bottom bracket.
The only specialised tool I have bought for this operation is the Park Tools BBT-30.4 Bottom Bracket Bearing Tool Set that is used to punch out the bearings from the inside. It also comes with a BB-30 "bushing set" that is used to push the new bearings back into the frame. This tool works fine at removing those BB30 bearings (with a 30mm inner diameter), but won't fit through the smaller BB86 unit that has a 24mm inner diameter (and a 42mm outer diameter). To remove these smaller bearings I fashioned a similar tool out of a large bolt, washer and a couple of nuts. For both tools the process was the same: press it against the bearing casing and repeatedly tap fairly hard with a wooden or plastic mallet, working around the bearing so that it comes out fairly squarely. I found that not much happened for the first dozen taps or so, but once it got going it moved fairly well.
This is the really nice part of the job. Make sure that the bearing shell on the frame is nice and clean and freshly greased, and the same for the bearings themselves. Line up the bearings against the frame, push your "head cup press" through and wind it up with the bushing set fitted. Now, you can buy your own press (fairly hefty and expensive), but I went mega-DIY and made my own out of a length of M12 stud and a few nuts. Utilising my bushing set and a spanner, I simply tightened it all up and the bearings smoothly slipped in.
There are obviously risks involved in applying a hammer to your pride and joy, so you need to have a good sense of exactly what you're doing. Proceed at your own risk! If you're unsure at any point, I recommend that you stop and take professional advice - preferably in person from a bike shop.