The hues of pine and oak fall in the same range of yellow and tan, but they aren't similar wood species, and combining them in a decor scheme usually involves stain. If you've just installed new oak cabinets and you're not interested in changing their color, you have to focus on the pine. Doors and windows include a lot of surface area, which makes the stain color and the way you apply it especially important.
Pine is not only lighter than natural oak, it's more porous and has a more irregular grain. It isn't difficult to find a pigment stain that will darken the color, but if you simply wipe that stain onto a freshly-sanded door or window, it will make blotches, especially around knots. You can avoid this by brushing on wood conditioner before you stain. Conditioner is a clear liquid that acts as a mild wood sealer, allowing the stain to remain near the surface and cover more evenly. It dries quickly, so this extra step doesn't add much time to the refinishing project.
Choosing the Stain
The best way to get a close match for your oak cabinets, which may themselves be stained, is to mix the stain yourself. You can do this by purchasing wood tone pigments from a paint store and mixing them in mineral spirits. Frequent tests on a pine board should lead to to the proper combination of pigments, which will probably include burnt sienna (orange) and burnt umber (brown). If you prefer to use a commercial stain, exercise caution when comparing color chips -- the actual color will probably appear darker on the doors and windows than on the chip.
Staining and Sealing
Whether you use a store-bought stain or mix your own, it's best to apply it with a paintbrush, starting at the top of the door or window and using long strokes that go with the grain. Wipe off the excess stain with a rag, going with the grain, while the stain is still wet. If you make your own stain with mineral spirits, you have to wipe often, because mineral spirits evaporate quickly. It's important to seal the wood soon after the stain dries to preserve color uniformity. Some woodworkers seal with shellac, which is easy to sand, but you can also use polyurethane or any other finish material.
Check the sheen on your cabinets before you buy your finish material so that you'll get a matching one, which could be full gloss, satin or flat. A light sanding with 220-grit sandpaper should precede your first finish coat and all subsequent ones except the last. If you're still having trouble with color blotching, one of the first finish coats can be a glaze, which you make by adding pigment to the finish. Glaze darkens the color somewhat, so you should avoid it if you already have a good color match. It needs at least one protective coat of clear finish.