How does a CDMA Rake Receiver work?
Simplifying somewhat (a lot, really) think of the training symbols as if we were sending a single pulse of a square wave. At the receiver, we receive a version of that that's been affected by multipath, so instead of a single pulse of the square wave, we receive several different versions of it, delayed by different amounts, and some of them (probably) inverted so they partially cancel each other, and so on.

In the rake fingers, we look for the single strongest version of the signal. Then we look for the next strongest, the next strongest, and so on, until we have the N strongest versions of the signal (N = number of rake fingers in the receiver).

Then we find the phase difference between each of the others and the last one of those to arrive. In each of the other rake fingers, we apply coefficients to get that finger's signal aligned/in phase with the last one. Then, of course, we combine them all together so they all reinforce each other instead of destructively canceling each other.

Of course, in real life we don't use a single pulse--but we still use a signal that makes it easy to recognize the starting point, stopping point, phase changes, etc.

As to how often to re-train: basically, you want to balance between two goals:

One one hand, you'd like to train as rarely as possible, so you devote as much time as possible to transmitting real data, and as little as possible doing training.

On the other hand, you'd like to to train as often as possible, to be sure you're making optimal use of the channel when you're transmitting actual data.

In most real-world systems, the time scale for re-training is on the order of tens of milliseconds or so.