Tools Needed
Washable Marker/Chalk
Bench Vice
Handheld File set (A three piece will do)
A thin strip of wood (At least 300mm long, and upto 8mm thick)
Heavy duty socket set
A sacrificial painters brush (25mm +)
Wire Brush- You'll be using this a lot, so you want a nice, firm brush with a comfortable handle.

Optional:
Gloves
Rags (For cleaning)
Vaseline (Petroleum Jelly will work just as well)
G clamps

Step 1: Health & Safety

IMPORTANT
Disconnect from the mains before removing the circular saw blade! Disconnecting the blade afterwards is also critical, because you don’t want fine powder inside the workings of the machine.

Removing the blade
A thin strip of wood can be clamped to the saw bed and against the
tooth, to ensure that the blade doesn't spin whilst you try to loosen the bolt that holds it in place.

Step 2: Preparations

1) Using the soft brush, apply Vaseline or petroleum jelly to the blade and allow to set for half an hour. This will help to break down the resin in the teeth.

2) Clamp the blade to the jig, then use WD40 and a wire brush to clean it. When brushing, go from the inside out, like you would if you were cleaning a CD. The rags will soak up the fine powder and residue as you go. Don’t be afraid to brush right up to the teeth!

The Help of a Jig...

I've prepared a jig that'll make this easier (Image 2). No need to write an Instructable for this one, yup, it's simply a 300mm baton with a short piece screwed to its end. A wingnut, coach bolt and washer will secure the saw blade to the baton; so you can keep it steady whilst sharpening. When you want to rotate the blade to reach the next tooth, it only takes a flick of the wingnut to release it.

Step 3: Sharpening

! Mark the first tooth (using the Chalk or Washable Marker) to save you sharpening teeth more than once.

! When filing, don't pull back and forth because this will blunt the file in no time at all. Instead, keep to nice forward strokes. You want a pleasant raspy sound, squeaking is usually a sign of incorrect use. Sharpen the top of the tooth until you see bright steel, and then the front. As you sharpen the teeth over the years, the profile of the teeth will become smaller. So the gullets will have to be deeper each time sharpening takes place, or the teeth will eventually appear misshapen.

Sharpening a Crosscut Blade?
Admittedly, this instructable has been written for those with a Rip Cutting blade; but I know a thing or two if you have a Crosscut back there:
Sharpen one tooth, skip a tooth, sharpen, skip - in light of the positive/negative way in which the tips are aligned. The teeth are aligned this way so the cut is wider than the width of the blade. If the blade was too thin, the friction (between the blade and the wood) would cause the blade to overheat and you'd be wasting a lot of power.

Crosscut blades tend to pack a lot more Oomph! An interesting article on the differences between the two can be found here