[I'm going to use .5-3 because that's how I learned it. Some people use 87-89 to describe the side bevel. Subtract 90 if you want]
First off, get:
-fine wet sandpaper
-an edge cutter for the side bevel you want (there's a few different kinds)
-a base guide for the bevel you want (there's a few different kinds)
-a sanding block
Base bevel is how quickly it engages, side is how hard it engages.
A 3 degree side bevel is really aggressive, a one degree will hardly engage. When you ski the ski, the edge becomes more dull. Logically, the more acute the angle the faster it will dull. As such, casual skiers get a less sharp bevel done than racers.
Slalom racers who get their skis tuned each day get 0.5 bottom, 3 side. This skis really well, but is hard to maintain.
Typical 1-3 tune a season skiers/boarders get a 1 bottom, 2 side as it's not super sharp, but will stay sharp longer.
Got these numbers from racewax.com:
Suggested Side Bevel Angles
Slalom -- 3 to 4 degrees
GS -- 2 to 3 degrees
Super G -- 2 to 3 degrees
All Mountain Expert -- 2.0 to 3.0 degrees
All Mountain Advanced -- 2.0 degrees
All Mountain Novice -- 1.0 degree
Snowboard Beginner -- 0 to 1.0 degrees
Snowboard Intermediate -- 1.0 degree
Snowboard Freerider -- 1.0 to 2.0 degrees
Snowboard Spinner -- 0 degree
Snowboard Halfpipe -- 1.0 degree
Snowboard Boardercross -- 1.0 to 2.0 degrees
Snowboard Slalom -- 2.0 to 3.0 degrees
Snowboard GS -- 2.0 degrees
Suggested Base Bevel Angles
Slalom -- 0 to 0.5 degrees
GS -- 0.5 to 0.75 degrees
Super G -- 0.75 to 1.0 degrees
All Mountain Expert -- 0.75 to 1.0 degrees
All Mountain Novice/Advanced -- 1.0 degree
Snowboard Beginner -- 1.0 to 2.0 degrees
Snowboard Intermediate -- 1.0 degree
Snowboard Freerider -- 1.0 degree
Snowboard Spinner -- 2.0+ degree
Snowboard Halfpipe -- 1.0 to 2.0 degrees (tip/tail); 0 to 1.0 degrees (underfoot)
Snowboard Boardercross -- 0 to 1.0 degrees
Snowboard Slalom -- 0 to 0.5 degrees
Snowboard GS -- 1.0 degree
So a 1 base, 2 side is a pretty safe bet if you don't know.
If you tune past 0.5 on the bottom it's going to be near impossible to get back to 0.5. Pick a degree for the bottom and use it for the life of the ski. One degree is what the vast majority of people use and is what I would suggest.
1) First, do the bottom. The bottom really won't change that much between tunes and you won't have to (and shouldn't) do much to it. Remember every time you tune you're taking material off of the ski, you only get a certain amount of tunes. When you do the bottom be very careful not to put too much pressure, but if there's oxidization you're going to have to.
1.5) Sometimes you'll have to remove some material from the sidewall in order to actually access the side edge in order to tune it. There is a tool for this. If you can't see the side edge then take sidewall off to expose it enough to tune it. Go easy, you can always take more.
2) Then do the sides, this will take longer than the base. It takes some practice to know how much to do but when there is a tiny (hardly visible) burr on the bottom it's done. If you can't see one don't worry you'll learn what to look for eventually. It will take a long time if there's been oxidization.
3) There is now a metal burr on the bottom of your skis, if you ski them like this they will ski horribly. You need to take this off.
4) Then rip a 2" width strip of sandpaper and wrap it around a metal file (so there's a two inch buldge on one part of the file) tape the other side of the file so it doesn't mess up your skis. Hold the file horizontally along the base of the ski (almost parallel, the bulge given by the sandpaper should account for the base degree. obviously don't let the file touch your base/other edge) and rub it along the base edge. This is to knock off the burr. This part takes longer than the rest of the tune combined. Rub the sandpaper along the base edge being careful to not push too hard and dull the edge, but also hard enough to knock off the burr. Just worry about the area up to and including the contact points of the ski, anything on the tip/tail will be accounted for later. Feel for a burr when you think you're done by sliding your fingers base-out, if they catch, then there's still a burr that you have to get rid of.
5) Now that you have a beautifully cut shiny edge without a burr, you have to dull the tips and tail. You WANT dull tips and tails. This is important for actually turning the ski. If you don't your tips and tails will catch when you're trying to turn. Super aggressive skiers hardly dull it at all because they want it to catch and turn more sharply. Take your sanding block and just rub around the metal edge on your tips and tail. Go as far as the contact points of the ski and stop there (otherwise this would all be for nothing!).
6) Wax 'em.
-You're going to cut the shit out of your hands if you do this often. It happens. I have a few scars. You'll get better at it. Don't use gloves though otherwise you won't be able to feel the burr.
-There are many different ways to tune skis.
-Knocking off the burr is probably the most important part of the tune.
-If you did a good job, the edge should take nail off your finger. Back of your hand towards the ski and slide your nail along it, if it takes a faint skim of nail it's sharp. It's kind of gross but it's the best way I've come across.
-If your skis are fully or mostly rockered, obviously don't sandblock all the way to your contact points otherwise your entire ski will be dull. But do sandblock far down the ski. Much farther than you would with cambered skis.
-Tuning rusty skis sucks.
-Do both skis at the same time. As in each step to each ski. This way your tune will be consistent. A consistent tune on both skis is better than two good tunes done differently. Consistency is key.
-Have the edge you're working on towards you at all times. You'll be flipping the ski a lot.
-The angle is actually called the bevel, prepare to be corrected if you call it the angle around ski techs.
-Some people say going tip to tail is important. I haven't ever noticed a difference.
Hope that's everything.