Pine chest of drawers?

If it’s finished, then just stripe, sand and stain. You can buy everything you need at your local paint or home improvement store. You say that the rest of your furniture is oak, so I would recommend that you take a drawer from another piece, or cabinet door, with you so that the person at the paint store can give you a good match.
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You can stain it an oak finish but if it is a knotty pine, the knots will show through. If you are just interested in getting it to match the oak in the room, you can take a drawer to the hardware store and they can try to match the stain.

Here is a photo of a pine plant stained with an oak colored stain:

http://www.lakesidewoodcrafts.com/c015e250.jpg

Here is the same stain on oak to give you an idea as to how the variety of wood changes the look

http://www.lakesidewoodcrafts.com/cf0c23e0.jpg
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As one of the other answerers pointed out, if the pine has lots of knots, it will look different no matter what color you restain it. Additionally, pine has other wood qualities that accept stain in a way that is almost unique to pine (there are other woods but pine is notorious for not accepting stain evenly), thus not lending itself to mimic oak easily. I’m not trying to put you off from ypuir project, just trying to set expectations. With that said, I’ll base my answer on what I would do to remove the old stain and recolor it to resemble the oak.

The chest may or may not have a sealer coat on it. This could be polyurethane (mineral oil based), shellac (alcohol based), or laquer (laquer solvent). This needs to be removed before the wood will accept the new stain. If the sealer is shellac or lacquer, the current coating will become gummy when the appropriate solvent is applied. If nothing happens after applying a little alcohol or laquer thinner in an inconspicuous area, it is probably polurethane. To remove a lot of polyurethane over a large area (like a chest), I would use Peel Away 7 or someother non toxic paint/urethane removal system. I just happen to like the peel away product.

If the chest has any leather work, or carvings, the removal process will get a bit more time consuming. Remove any metal fasteners, handles, hinge, etc. before stripping the varnish. This will also make the rest of the prep work easier.

The paint remover won’t remove the stain, it just strips the surface of the wood. You will have to bleach it out to get the wood clear enough to accept the new stain without any color interactions.
After bleaching, you will need to lightly sand all of the surfaces of the chest as the water and bleach raise the grain of the wood and make it rough to the touch. If the original stain is light and you are planning on a similar shade just darker to match the oak, you may not need to bleach.

Once you have the chest prepped and ready for restaining, there are somethings you can do to minimize the "pine effect." That is the uneveness and blotchiness with which pine accepts stain.
I would try each of these methods a scrap piece of pine to see which produces the desired effect. Unfortunately, the scrap and chest are still 2 different peices of wood and even if they are the same species of tree, they may not accept the stain the same way. Once you determine which method works for you, you’ll have to test it again on the chest (maybe on the bottom).

The first is try a wood conditioner before staining. These are sold by the large stain companies (Minwax for example). The conditioner is just a very dilute sealant coat.

The second method is to use a gel stain. These are also widely available (Minwax makes one) and I’ve had better results with this method but the materials are a little more toxic. A gel stain is exactly what it sounds like stain in gel form. So it’s goopy and you have to spread it and let it set for a while. The benefit however is it produces a more even stain color. The negative here is I’m not sure you can get someone to custom color match a stain in gel form. You may be on your own for that.

The last method is to use a dye instead of a stain. Dyes actually color the wood fiber whereas a stain uses a binder to get "stuck" to the wood fiber. This method is the least toxic of the 3, since dye can be alcohol, or water based (there are other dye solvents) it is also least affected by the wood’s grain properties. They come in an almost unlimited amount of colors, but you may have to spend more time matching the color and you would probably have to do the color matching . Also, this method will probably need the wood bleached in order to see the dye without color interactions.
Dyes are avialable by mail order from any woodworker supply company. Also, you could try Lockwood Dyes (http://www.wdlockwood.com/).

Once the color is on, you should apply a sealer coat (poly, shellac, or laquer). The dye’s can be released if the sealer coat has the same solvent–a water based poly would lift and "muddy" a water based dye especially if you are brushing the sealer on. Try spraying your first coat of poly or what ever sealer you choose or try using a sealer with a different solvent from the dye just make sure you allwo the dye enough time to dry before applying the sealer..

Good luck!
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Ok..first of all oak is a wood not a stain. Oak can be stained all different colours as can pine, or ash, or birch…..you get the picture. If you stain pine, the same colour of stain used on your oak there is a good chance the colour will not match because oak and pine are two different woods. If you want to match the stain colour of the oak, this can be done, but usually you will have to test a couple of colours first to match the colour on the other wood. It will not look the same because of the grain in the woods being different, but the actual colour can be matched. What you will end up with is oak and pine with the same colour, but not look like the same wood because they are totally different.
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