I have some extra pasta, cooked.
I have no extra sauce to put the pasta in.
What's the best way to preserve it so it lasts for a day or hopefully two without getting dry or rotten?
Toss in oil and do not salt. This should help keep the pasta from drying out. Refrigerate until you are ready to use it. Before use, quickly reheat the pasta in boiling water or in a hot pan, which will give the starch a fresher, "just cooked" texture (this is the same reason that you toast old bread)
Besides Kevin's recommendation, if it's a smaller pasta (not long strands or sheets), you can turn it into a pasta salad; there are plenty of recipes online, and it's often better if it's had a day or two to sit for the flavors to meld.
You can also freeze individual portions in sandwich bags, then heat back up in boiling water. A lot of resturants (of the lower end) do this with their spaghetti. Since it doesn't require any additions it won't change your flavor profile. Stays good for about 2 weeks, after that you will start to notice texture change.