There is quite a lot of information and discussion (in books and on the web) about proper yeast pitching rates. Maybe it's the wealth of information that makes it so confusing, but I run into many people who are completely lost about how much yeast to pitch. Hopefully the following makes the math a little easier to understand. When you'd rather skip the math, the Pitching Rate Calculator does it for you.
Ales & lagers
The general consensus is to pitch around 1 million cells of viable yeast per milliliter of wort per degree Plato, a little less for an ale, a little more for a lager. George Fix gives about 1.5 million for a lager and 0.75 million for an ale in An Analysis of Brewing Techniques. Other literature cites slightly higher amounts. I go with Fix's numbers, and that's what the pitching calculator uses.
The math
If you're curious, here's the simple math. For an ale you want about 0.75 million viable cells per ml per degree Plato (1.5 million for a lager):
(0.75 million) × (ml of wort) × (°Plato)
There are about 3,785 ml in a gallon, so about 20,000 ml in 5.25 gallons. A degree Plato is about 1.004 of OG, so divide the decimal part of the OG by 4 (1.048 ≈ 12°P). So for 1.048 wort into 5.25 gallons: 750,000 × 20,000 × 12 = 180,000,000,000 (about 180 billion cells).
As an easy estimate, you need about 15 billion cells per degree Plato, or about 4 billion per point of OG, when pitching into a little over 5 gallons. A quick back-of-the-envelope version: roughly 0.75 billion cells per point of gravity per gallon for an ale; double it to 1.5 billion for a lager.
Pitching from packs or dry yeast
Both White Labs and Wyeast make fantastic products. You can't go wrong with either. Each brand has its own strains, pluses, and minuses, but neither is better across the board. Use whichever your local shop carries if you need a way to decide.
The packaging has changed since I first wrote this, and for the better. White Labs has retired the old vials and tubes. Their liquid yeast now ships as PurePitch Next Generation pouches, and a single homebrew pouch is designed to be a complete pitch for about 5 gallons (19 L) of standard-gravity ale, at better than 95% viability. Wyeast's Activator smack-pack works the same way: a minimum of 100 billion cells, one pack sized for direct pitching into 5 to 6 gallons (19–22 L) of standard wort. So for a 1.048 ale into 5.5 gallons (21 L), one fresh pack of either is right in the ballpark, no starter required. The catch is that this assumes a standard-gravity ale and fresh yeast. Step up to a big beer or a lager, or reach for a pack that has been sitting a few months, and you are back to needing more cells: a second pack, or a starter.
Dry yeast keeps getting better and cleaner. I prefer liquid yeast, but dry is cheap, convenient, and in most cases needs no starter. The cell count is where people get tangled up, because the number printed on the pack is a guaranteed minimum, not a measurement of what's actually in there. Fermentis guarantees at least 10 billion viable cells per gram for their ale strains and 6 billion for lagers; Lallemand guarantees at least 5 billion for most strains. Those are the floors the makers promise to clear. The reality in a fresh, well-handled pack is usually higher, up to around 20 billion per gram, depending on the strain, how recently it was produced, and how it was stored and shipped. I've counted dry yeast many times and consistently land near that upper figure, and Dr. Clayton Cone and others I trust have found the same. So the practical point is that you generally have more live yeast than the printed minimum suggests, not less. Rather than guess where in that range your pack falls, let the Yeast Pitching Rate Calculator sort it out: give it the gravity, the volume, and the production date, and it tells you how much to weigh out.
For most standard-gravity worts you can skip rehydrating altogether and sprinkle the dry yeast straight on top, but in a big beer it matters, and there's a right way to do it. I've put the whole process (when it's worth the trouble, the water to use, and the step-by-step) in a separate guide to rehydrating dry yeast.
And for dry yeast, skip the starter. A starter just burns through the reserves the maker packed in, and the yeast is cheap enough that a second pack is the easier, better fix when you need more cells. The one time a starter earns its keep is a pack you have real reason to think is old or mishandled. There, growing the survivors back up can be worth the trouble.
Starters & stir plates
One way to get the proper number of active cells is a starter. The little nutrient pack inside a Wyeast smack pack does not replace a starter. It's there to jump-start metabolism and act as a built-in viability test.
Starters are easy, especially with a borosilicate Erlenmeyer flask. Keep the OG around 1.030–1.040. You don't want a high-gravity starter. As a ballpark, about 6 ounces by weight of DME to 2 quarts of water; in metric, a 10-to-1 ratio (1 g DME per 10 ml final volume). Add DME and water to the flask, cap with foil, drop in a pinch of nutrient, and boil gently on the burner for 15 minutes, then cool. Add O₂ if you have it, or at least shake every few hours; a stir plate is better still (around twice the yeast of a non-stirred starter).
You'll get more growth the warmer the starter (up to 90°F+), but viability suffers at those temps. For lagers this means more petite mutants and poor flocculation. Keep ale starters in the mid-70s°F and lager starters a few degrees lower. If you'll pitch the whole starter, keep it near the pitch temperature: Dr. Cone suggests within 15°F, and Neva Parker (White Labs) suggests a maximum swing of 10°F, ideally 5°F. I agree with Neva. Pitching warm yeast into cool wort shocks them and can create petite mutants that never ferment properly and throw excess H₂S. If you run starters warm, let them fully ferment out, let the yeast drop, chill, then pitch just the yeast.
Wyeast says starters reach maximum cell density within 12–18 hours, which matches my experience; waiting 24–36 hours returns little. I pitch while still very active, usually 8–18 hours in, so the starter is ready when the wort is. There's no need to make one a week ahead. I pitch the whole starter, liquid and all, up to a certain size. If you want it fully fermented so you don't pitch the liquid, use a larger starter, let it run its full cycle over several days, chill, decant the beer, and pitch just the yeast. For smaller starters, just pitch the entire active starter within about 6–12 hours of inoculation.
Greg Doss (Wyeast) reported roughly these results within 12–18 hours from an Activator pack: a 1-liter starter ≈ 150 billion cells; a 2-liter starter ≈ 200 billion; and a 1-liter step into a 4-liter starter ≈ 400 billion. Practical experience suggests these are at least in the ballpark. Why don't 1-liter starters produce more, even with a stir plate? There simply isn't enough food to build more yeast, no matter how much O₂ and nutrient you add.
Repitching yeast
If you've brewed more than one batch, you've seen the huge pile of yeast left in the fermenter. With excellent sanitation throughout and proper nutrition (including O₂), that's a gold mine of healthy yeast. Don't reuse the whole thing, and don't just dump a new batch onto the cake. Yeast need some growth for the right ester profile, and while too big a pitch beats too little, it's easy to figure out how much you need and pitch just that.
There are about 4.5 billion cells in 1 ml of yeast solids (no excess liquid). Per Fix, only about 25% of a slurry's mass is yeast solids (less if there's a lot of trub). The catch is you can't tell viability without the equipment to test and count, so this gets a bit like black magic: how old is the yeast, how stressful was its last fermentation, did it have the right environment and nutrients? Fresh, healthy yeast off a previous batch might be around 90%+ viable, dropping fairly quickly without proper storage and depending on strain. Unless you're testing, make an educated guess and keep good notes. Starting in the 80–90% range usually isn't far off. Use the Pitching Rate Calculator to figure out how much slurry you need. If viability is much below 90%, consider tossing it; if you really want to use it, pitch it into starter wort to wake the viable cells, then decant the active portion off the dead cells.