The key to base-running is understanding that there is a distinction between times when you are supposed to go somewhere and others when you may voluntarily go somewhere. This distinction depends on the a priori base-configuration (which base am I on?, are other bases also occupied?) and what happened with the batter's hit (was it caught before hitting the ground?). This distinction is important to base-runners (and to fielders) because it dictates the ways in which you may be put out. Let's call the base to which you're supposed to go, or on which you're supposed to stay, the ``mandatory base" (not baseball jargon, just a phrase I now made up). In any situation, there will only ever be one mandatory base for each runner.
in The instant you safely touch your mandatory base, it loses its status and you no longer have any mandatory base. (Also note that once you have touched home plate safely, you have already scored and are no longer a base-runner.) As an example, let's look at the batter. After she hits the ball (and it isn't caught on the fly), her mandatory base is 1B; she can be retired in either of the two ways above. If she reaches 1B safely and decides to continue on, she must be tagged to be put out.
The (theoretically) easiest case for a base-runner is when the batter's hit is caught on the fly. After the catch, your mandatory base is the one you were on before the pitch, but you may voluntarily try to advance to some further base (again, after the catch -- this is called tagging up). This means that if you started to run before the ball was caught, and the fielders get the ball back to your original base and touch it before you can go back and touch it, you'll be out -- you don't need to be tagged. If you weren't touching the base when the ball was caught but still want to advance, you'll have to go back and touch it before advancing. Operationally, the tricky bit for the base-runner is knowing whether the ball will be caught or not. If, for example, a fielder drops a catch, your mandatory base could well change instantly, and through no fault of your own you may become out by a mile (more later).
When the batter's hit lands in fair territory without being caught (either as a ground ball in/through the infield or a hit to the outfield that drops in) is a little more complicated. Now your mandatory base will depend on your current base and the occupation of bases behind you (occupation of bases ahead of you never affect your mandatory base):
Put another way, on a ground ball, the batter's mandatory base is 1B. If someone is already there, he has to vacate it to make room for the batter, and his mandatory base becomes 2B. The same argument would apply if someone else were also already on 2B at the time; she has to vacate 2B for the runner coming from 1B, and her mandatory base would become 3B. So, on a ground ball, your mandatory base is the next one if someone else's mandatory base is your current one, with this causal chain being traced back ulitmately to the batter.
When you have a mandatory base on a ground ball, the rules for being put out at your mandatory base are as above. This situation is called a force play; if a fielder holding the ball touches your mandatory base before you do, you're forced out (officially, the batter doesn't get statistical credit for a hit, even though he may well be standing safely at first). If you don't have a mandatory base, or try to advance beyond your mandatory base, you must be tagged out. The figures (a) - (g) below illustrate all possible configurations; you are green, occupied bases are black, and your mandatory base, if any, is red. To be repetitive, you can be forced out at the red base; at all others you need to be tagged out.
There are also some ``2-order" ways of becoming out as a
base-runner, which we can go over in more detail should they arise in
actual play:
campbell@jive.nl