Rico has the right idea. For mine I do the following (and am making it a part of my tool service practice also). Take the head off the hammer. Put the head in a bucket of sand mixed with oil (even old engine change stuff is okay) to soak.
Take the handle and strip the old finish off, to include any handle grab material (we all know how duct tape suddenly appears ). Once the handle is stripped, you have a couple of options. 1 is the linseed oil option as mentioned. Just make sure you use boiled, not raw, linseed oil. Raw stuff has a nasty habit of spotaneous combustion if kept in a confined area and subjected to heat (like in a tool box in the back of a truck

). Using the linseed oil, brush it on, not dip it or let it soak by putting it in a tray. You want penetration of the wood fiber, not a cellulose sponge that takes a week to dry out. Once the handle has had 3 to 4 coats, sanding in between w/ a 400 to 600 grit paper, you can set it aside for a while to work on the head.
The head needs to be cleaned using any stripping agent you want. The soaking in the oil will have loosened up most if not all of the old rust and corrosion fairly quickly and ease it off when you start the next step. Unless the head is THAT badly rusted, or corroded, the stripping agent shouldn't matter. I use both mechanical (a open face grinder w/ an abrasive wheel) and a non-toxic chemical (can't say openly but you probably drink it at least once a week and strips corrosion of the bottom of copper pots like magic). And be sure when doing this stripping, no matter what the process, you keep the work area well ventilated. A great many tools, not just hammers, were made using LEAD-BASED PAINTS as a finish. 'Nuff said (I hope

).
Once the head is stripped, depending on the environment in Oregon you are working under (ocean, woods etc) it is not a bad idea to use a corrosion inhibiting primer on the whole of the head. Just make sure you put some old newspaper in the handle slot before you spray, not dip !!!! After the primer a good spray of either epoxy based or engine paint is a very good idea. The epoxy paint takes a beating before it starts to chip and reveal open metal. The engine paint is a bit more 'fragile' but it tends to take more heat over time as opposed to the epoxy. Either way, the hammer head will probably out-live you and me.
Once the handle and the head are done make sure you have a piece of 400 grit sandpaper handy. Dry fit the handle and head for a good fit. Sand for any rough spots (there shouldn't be any at this point). Using the Gorilla glue (no, it's not an endorsement, just in response to the post), sand the top of the handle to raise the grain just a bit. Once raised, spray a bit of water on the area (believe it or not a kid's water pistol is perfect for this). Apply the glue to the wood and IMMEDIATELY slide the head on to the handle. Placing the handle in a vise or the head in a vise is a good idea. Once the handle is in place, in a vise, put a small block of wood on the head or handle bottom. Tap the block sufficient to seat the handle and have a small bit of glue seep out form the head/handle joint. Wipe and let set for about 3 to 4 hours (Gorilla glue takes time to set up despite the label's rah-rah).
If you want to re-use an existing handle that has shrunk you can use the method above. Just make sure you have a solid wood wedge to insert into the handle's slot. Like shiming a door, get it in early, tap it to seat and when finished, cut the excess off. But beforewarned !!! Gorilla glue expands like mad. And it don't care what is in the way. If the handle or metal have any weakness at all, the glue will find it and rip it apart as a part of the drying/expansion process. I've seen this stuff rip apart fence posts (6x6's) like they were cotton candy

.
If you are worried about that possibility, use the epoxy glue method. Again, prep, prime, paint and sand. But when you get ready to 'glue' have everything ready and within reach. Epoxy, depending on the brand and the conditions used in, will set-up in less than 45 seconds. You need to have the handle or the head in the vise, with the wedge, wood block and hammer right there. Sand the head/handle area. Wipe but do not remove any grain raised !!!! Mix the epoxy, spread on the handle/head area and slip the head on. If a wedge is going to be used, now's the time to get it in and tap it for seating. Once the seating is done you should have a finished hammer. Cut off the excess wedge material and off you go. Any excess epoxy that seeped out from the head/handle joint is going to be virtully impossible to remove so either be careful when glueing or be prepared to live with the inevitable results. Me personally, I would wait a good hour for the epoxy to set up. Just good safety practice

.
Mike