I'm going to stain my birch cocktail cab a shade of blue.
Are you talking an aniline dye or one of those tinted stains (Minwax, I think, is who makes those)
My plan is to put on several light coats of stain and sand in between each coat and then seal it with several light coats of poly. The goal is to be able to have that smoth glass-like finish and to not have to worry about spilling my beer on it.
Stain is not like paint. If you want a darker shade, let it sit on the wood longer. If you want a darker color after waiting as long as you think is necessary, try it again. After a certain point (usually the second long-waiting-time coat) you won't improve the darkness and risk ruining the piece.
I've heard that finishing a piece of furniture takes some time
Time, patience, work, and the right tools.
1. Is there a recommended brand/type of stain and poly for this project?
2. How many coats for the stain and the poly is typical?
3. What type of grit should the sandpaper be for sanding in between coats?
4. Should I invest in an orbital sander or is doing it by hand sufficient?
5. Any other tips?
1. Use a wood conditioner (Minwax makes one, other techniques aren't worth going into - they'll just add confusion....but you CAN use something other than theirs). It'll help even out the stain coloring.
2. 1 of stain (mebbe 2) poly depends on whether you like it or not. 1-3 is normal.
3. Make sure your poly has cured, otherwise your sandpaper will gum up. Use progressively finer grits. Start with 600-ish on the first go-round. Follow it up with something 800-1000-ish. On your final "I think this is it" coat, after the finest grit, clean it all off, apply a coat of rubbing compound and buff that off, and finish with a coat of wax. I've found auto wax works just fine for that. The furniture wax is just overpriced and does exactly the same thing

4. An ORBITAL sander isn't the way to go. A
RANDOM-ORBITAL sander will work just fine. There's a definite difference, and I think unless you're using auto-body equipment, an ORBITAL sander would be hard to find.
5. Get several plastic drop cloths. Tape 'em up. Make yourself a "booth" to do this work in. Dust will be your enemy.
If you want to make this something you'll feel comfortable setting your beer on, use something called "Spar varnish" instead of polyurethane. It's tougher and more resistant to spills/liquid sitting atop it. Standard poly may develop a ring from your beer mug. Spar varnish is used for outdoor furniture and marine applications (prolly other stuff, but those are two biggies)
Do both sides. (don't have to sand/seal/wax the unseen side to the same quality, but apply the same products to both sides) You may warp your wood if you only do one side (after some time, and chances aren't huge, but it may happen, and if you want to avoid it, it probably WILL happen

)
As Wade said, don't load the finish on all at once, light coats to build up are better. One thick coat may not cure fully for a week or more!
If you want a darker initial stain color, sand one piece of scrap wood with 60 grit, one with 100 grit, one with 200, and one with 400. The lower the number, the darker your stain will be (i.e. 60 should be darker than 400). After some grits, the color looks like ass. You'll need to experiment to find out what you'll like.
DO NOT UNDER ANY CIRCUMSTANCES USE STEEL WOOL! If some fibers come off and embed themselves in your wood, over time they may rust, at which point they will make themselves noticeable and quite hideous to you. The chances of that happening aren't worth the hassle. Use a Scotch-Brite pad (they're the green scrub pads you can find at Wal-Mart....different "grits" can be found....black is coarsest, green is medium coarse, white is fine....I think they make a blue which is ultra-fine, but I may be off my rocker on that one

If you really want a nice finish, spray the poly/varnish.