The scanner is a powerful tool that can be used to find other ships in space quickly or to gauge up your opposition. All members of the fleet should have basic knowledge of the directional scanner, and this is what this post seeks to provide. Advanced tricks and techniques are nice to have, so post your own tidbits at the end :D

Parts of the scanner
The scanner consists of three different scanning systems. This guide will only concern itself with the middle "Directional Scan" tab. Ask me about the other two if you're curious. The Directional scan tab has a few components. One is the range in km. Vary this for range scanning, but set to max range for most uses. Max range can be put in by putting in a lot of 9's. Angle will be varied for directional scanning but will be at 360 for range scanning. Note that when you slide over the angle tab, a new scan is performed. A new scan is not performed when you put in a new range. You must then hit the "scan" button. The readout at the bottom gives you the name of the object (ship name) the type, and the distance, if it's on hte same grid as you are. Finally, the "use overview settings" box should always be checked. Note that the ship name is the name you give to your ship. If all ships of an op have the same pattern, like the proposed full stop for us, it makes it easy to identify which ships belong to who and to size up enemy forces. Ideally, this identifier should be discreet, so that the ability to size up your force is denied to the opponent.

Overview Settings
Since you will have "use over view settings" checked 99% of the time, your overview settings should be good. Set them to show ships, control towers and mobile bubbles only. The ships part is obvious, we want to find ships. The control towers prevents you from warping in on a ship when it's at a POS (or at least gives you some warning). The mobile bubbles setting lets you spot gatecamps if you're scouting ahead. For range scanning, you'll want to enable planets, but this is best done manually.

Note that an interdictor's bubble is not counted as a warp bubble, so if you see an interdictor or smell a trap, do a scan for Scan Probes. See the end of this post

Range Scanning
Use range scanning if you need to get a target down to a planet. Of course, this assumes that the target is AT a planet (or around it anyway, belts, moons, etc). As such, it's only really useful for raiding and pirating. Set your overview to include planets and scan. Halve your range (about, no need to be precise, I usually only change the first character) and scan again. Note which planets disappeared. If your target disappeared also, it's around one of those. If it isn't it's not.

The logic here is to use a "halving" mechanism, where you add or subtract half of your deviation. So, let's say my range is 15,176,134km, and my target is at 4,332,234. My range selection will go like this

15,176,134 (first scan)
7,176,134 (just halve the 15)
3,176,134 (halve the 7) <--target disappears, so I know its more than 3m and less tahn 7m
5,176,134 (halve the diff and add) <--target back on scanner
4,176,134 (target still not on scanner)
4,876,134 (only changed one number, add about half the difference) <-target on scanner
4,476,134 (target still on scanner)
4,376,134 (still on scanner)
4,276,134 (not on scanner)
4,326,134 (not on scanner)
4,346,134 (on scanner)
4,336,134 (on scanner), but can't drop any lower, so move to the right a spot
4,330,134 (not on scanner)
4,333,134 (on scanner)
4,332,134 (not on scanner), move over a place
4,332,634 (on scanner)
4,332,334 (on scanner)
4,332,234 (on scanner)
4,332,184 (not on scanner)
4,332,214 (not on scanner)
4,332,224 (not on scanner)
4,332,232 (not on scanner)
4,332,233 (not on scanner)
4,332,234 (on scanner, found)

Obviously this is a lengthy mechanism, but since you're also keeping track of planets, you don't really have to get it down to 1km (in fact, it's best not to). Usually, within a few million will be sufficient.

Directional scanning
Directional scanning is useful to pinpoint things in space. It's much more precise than range scanning because it scans an angular cone of space rather than a sphere. The trick here is to rotate your camera, not your ship. Your camera controls where the scan is directed, so you need to place your ship over the area you want to scan. So, you want to scan a planet? Rotate your camera until your ship is sitting over that planet and hit "scan." It's usually a good idea to start from wider angles and get narrower. Holding down ALT will let you see the exact center of your ship in brackets [ ]. It does do funny things with the camera though.

Scanning for Scan Probes
When you're safespotted, you can set your range to 10AU (1,500,000,000km) and turn off "use overview settings." This will scan everything in range, including scan probes. If you see any in the list, it's best to switch safespots.
Also, 150m km = AU. The max range of the scanner is something like 13.4 AU.