Like most games, the skills in Fallout 3 tend to work best if you choose a few areas to specialize in. Keep in mind that skills are associated with attributes, so you'll have an easier time maxing out skills that are associated with attributes in which you excel.
You'll want to have at least one bread-and-butter combat skill. This will be either Small Guns, Energy Weapons, or Melee Weapons. One is just as effective as the others, though Melee Weapons will require you to get up close, and you'll have to be a bit more careful to make sure that happens. If you're a real min-maxer, then remember that Small Guns is associated with Agility, and if you boost Agility you'll not only increase your combat skills but also your action points for use in VATS. Also keep in mind that most powered armors will give you an Agility penalty, but no such penalty exists for Perception.
When it comes to skills like Speech, Lockpick, and Science, I suggest either maxing them out or ignoring them. The really interesting and profitable things that can be accessed with these skills will require you to be highly proficient in them. There aren't many interesting things to be found in safes that are of merely "Average" difficulty, for example.
If you read the manual, you probably realized that a lot of Perks that are available also increase skills. Some of these Perks increase skills so much that it seems inadvisable to actually invest many skill points into a skill. The most obvious example is Size Matters, which boosts your Big Guns skills by a full fifteen points. If you're focusing on Big Guns anyway, then taking this Perk effectively doubles the amount of skill points you are given for the level, assuming you have average intelligence and would normally gain fifteen skill points.
In the long run, using Perks for skills can be very effective, due to the relative weakness of many Perks and the fact that not all Perks are going to be relevant to the way you're building your character.
Also remember that Items which increase your skills beyond 100 aren't going to give you any additional benefit. If you plan on always using an item that gives you an extra five points in Science, for example, don't increase the base skill beyond 95.
The most important advice I can give regarding skills is this: Have A Plan. If you don't have a plan, then you will waste your points as you decide to shape your character in one direction, and then change to focus on some other aspect. In fact, you should have a good idea of who your character will grow to be before you start the game. It is critical that you put at least five points into your main combat skill every level, and it is also important that you level up your favorite non-combat skills with similar aggressiveness. Maxing your lockpick skill out won't do you that much good if you're already 50 hours into the game, unless you feel like revisiting every locked safe you couldn't unlock because your skill was to low.
Specialize, plan, and survive. Good luck in the Wasteland!