Be sure to scroll down... there may be more than one question on this page!
I can try to get you started but I can't guarantee that it will be an easy job or that it may not turn into "quicksand"... my favorite expression for a job that looks small but grows to gargantuan proportions! I hope to give you a good sense of what this job entails and some potential problems so you can judge whether or not you really want to tackle it yourself.
Rot repair is a two-step process... removing the rotten wood and replacing it. That at least sounds easy! And some rot repairs ARE fairly easy, such as wood moldings or siding, since the entire rotten area is easily accessible. Thresholds, however, can be a problem when the rot extends beneath them. Depending on the design of your home, there is always the chance that other wood members will also be rotten; these may or may not be accessible. For example, if you have concrete steps outside your door, there is often rot in the wood behind them. It is almost impossible to remove all the rotten wood in these situations, so the only "easy" solution is to get out as much rot as possible and fill the area with a concrete patching cement. This will give a solid base that will never rot again. But I am getting off track...
The first step in this repair is to remove the old funky threshold. This is done by making two cuts with a circular saw across the width of the threshold approximately four inches from each side of the door frame (or as close as the body of your saw will allow). You should not cut too deeply... just enough to get through the threshold. If you have to make multiple cuts along the same line, that is better than overdoing it! Make sure your saw has a carbide blade... there is a chance you will run into nails and if your blade isn't carbide it will most likely be ready for the trash heap should you hit one.
You should now be able to remove the center part of the threshold, leaving a small piece on either side. If the remaining pieces do not come out easily, they are probably held in by nails to the door frame. Trying to pry them out may cause unnecessary and even severe damage to the door frame. Old, dry door frames can split severely if you were to try to force the threshold out. Instead, get a wood chisel at least an inch wide. Split the threshold up into smaller pieces (along the length) by hammering the chisel into the grain of the wood from the top. The grain may not be visible if the threshold is painted, but it runs from door jamb to door jamb. The threshold will split along the grain into pieces. Keep splitting it until it is completely free of the nails holding it into the door frame.
You might be able to save yourself some splitting if there is a gap between the door jambs and the threshold pieces. This gap will allow you to insert a hacksaw blade and cut the nails off. You can get a special hacksaw blade handle for this purpose or lock a hacksaw blade into a set of ViseGrips.
Once the threshold is completely removed, you will know whether or not you have a more severe rot problem. This is where it gets complicated, since there are too many possible repairs to go into here. So lets pretend that the rot does not extend beyond the threshold... phew! Now your job is to install a new threshold. Using the center piece of the old threshold as a sample, take it to the lumberyard or home store to choose a replacement. The only other information you will need is the width of your door.
Exterior oak thresholds are shaped like a squat, fat "T" with two small ears that protrude under the outside staff molding. Thresholds precut into this shape are available. Whether you will have to modify it or even make one yourself from a length of raw threshold is a big question mark. Chances are, though, there will be some modification needed to fit it under the frame.
We are going to make a leap of faith (and time) and assume that you have properly cut and test fit your replacement threshold. Now the trick is installing it in such a way that it will be as good and sturdy as new. And it is a trick! Since the threshold is slightly tilted towards the outside to run off rain water, it is not just a matter of sliding it under the door jambs and nailing it in place. NO... that would be too easy. To raise and hold the threshold securely, you insert strips of wood... a.k.a. shims... and insert them under the threshold to give it the support down under.
Because of the threshold's angle, it is impossible to insert a shim to hold up the inner edge of the threshold while it is in place. Instead, you will have to attach a shim or shims along the "two-by" frame under the inside edge of the threshold. The width of these shims should be no more than 1 1/2 to 2 inches. It will take a few tries to get the shim's thickness right. Depending on how level the frame is, you might be able to use a single strip of wood along the entire length of the threshold, or you might have to vary the thickness of the shim. Keep your goal in mind… to have the threshold held up strongly by this inner shim against the bottom of the door jambs. A really tight fit might require you to tap the threshold into place with a hammer (use a piece of wood between the hammer and threshold to protect the threshold from damage).
Once you have a fit that is tight and will stand up to weight, remove the threshold and put construction adhesive on the shim(s). Tap the threshold back into place (it will slide in easier with the lubrication of the construction adhesive) and install additional shims under the outside edge of the threshold, tapping them into place until you get a similarly tight fit against the door jambs. A little construction adhesive on them would also not hurt! These shims should be inserted under both door jambs and at least two additional ones spaced out underneath the threshold. Don't warp the threshold by using overly thick shims!
As a final step, predrill the threshold and shims and nail through it, the shims and into the solid framing below using 3" galvanized finishing nails. The predrilled holes through the threshold should be the same size as the body or "shank" of the nails. Though the heads are small on finishing nails, the oak is so hard and the construction adhesive so strong that this total fastener package will hold your new threshold securely in place.