Hello
I'm a furniture builder and a carpenter by trade, and I use the same process anytime I am applying a finish to a brand newpiece.
First, I sand the project down, going WITH the grain, with 100 grit sand paper to get rid of any minor imperfections. Follow that with 180 grit sand paper to begin smoothing it all out, and finish with 220 grit. After that, I blow the project off with compressed air and wipe it down with a tack cloth (Found in the stain/polyurethane section of your local home improvement store) that will pick up all the dust left behind that the compressed air did not get. If you are going to stain the project, now is the time to do it. I use Minwax stains that come in the yellow cans, as i have had the best results with it, and why change what works? I generally apply two coats of stain, applied with either a paint brush or an old t-shirt. Let the stain penetrate the wood for about 5-10 minutes, and then wipe off the excess with a separate rag. Once I am happy with the color, I let it dry overnight to ensure uniformity, and then I begin applying polyurethane. I use a rattle-can spray form of Minwax semi-gloss. I do not like brush-on styles, I have found them to leave brush marks behind, and they have a higher chance of running. I spray on one light coat, and let it dry for about an hour. Then, I sand ACROSS the grain very lightly with 220 grit sandpaper. Do not use a power sander like an orbital. What this does is remove the microscopic fibers of wood that tend to "Rise up" after the first coat. That's why it feels a bit bumpy after the first coat of spray. A very light sanding with 220 grit sand paper across the grain will take care of it. Once that's done, wipe down with another tack cloth, and spray on your second coat. These first two need to be light, otherwise they are just going to run and sag, and look awful. Repeat the process for the third and final coat, this coat will be a bit heavier because this is the coat that will be offering the most protection and shine. Do not sand after the third coat. I let that dry overnight and that's all there is to it. It sounds more complex than it really is, but if you take your time and pay attention to details, even your first "Finish" job will look like a masterpiece. One final tip, do NOT use fans to try to make the stain or sealer dry faster. You risk kicking up dust that will get into the finish, and then you will have to start all over. Just be patient and let them dry on their own.
I hope this helps you out. If you have any questions, don't hesitate to ask! Good luck, and remember: If you rush it, you will regret it.
