Let's start with example #1:
So far we have a solution to all of Cross+F2L. You should be able to recall the sequence accurately: you will trace every LL piece through it.

First, find the UF edge. In this case, it's WR, and located at DF in the scramble.

Now, take the principal sticker (the color of the U face) and trace it through the solve.

It lands at RU. Since we really care about the principal sticker, remember its position as the first LL "key."

If you trace the other LL edges, you will find them to end up so (in clockwise order from UF):
OLL locations of the traced UL (WG), UB (WO), and UR (WB) edges

Partial Tracing

I'm emphasizing this because you should only try it if you are extremely careful: Only do this if you have done a lot speed BLD solves with 100% success rate, F2L has been blazing, and you are expecting the world record for memorization.
Just kidding. But really, only try this if you are going for quick memorization and think you can be (or are) careful enough. It's normally always better to check with independent redundancy to make sure that no two pieces land at the same spot.
The idea is based on the principle that if 12 object occupy 12 spots and you know the location of 11 of them, then you can tell what the last is. So when you get to LL, you you can trace three edges, and the last one has to take the remaining spot. It also has to satisfy parity for orientation.
So if in example 1 you traced the UF, UL, and UB edges (1, 2, 3), you would know that UR (#4) has to be at UL. Also, since there are already an even number of edges flipped on LL (and, therefore, the whole cube), you know that in this case it is oriented correctly.
If you traced only two edges, you would not know which goes where (except from corners, by cycle parity, see later) and how they are oriented (both could be flipped from the correct state, and nothing can help you except to trace one of them).
The same applies for corners. Trace three, and the fourth has to be in the remaining spot, and be oriented to form a proper OLL.
There are several points of caution:

• If you make a mistake in tracing a piece, you will either place the fourth one incorrectly, orient it incorrectly, or both. CO is tricky to follow accurately, for example, and a tiny 1/3 rotation error anywhere will ruin the entire solve.
• Also, you will not be able to tell if you made any errors on F2L. If you flipped an edge during placement, you would assume the incorrect orientation for the fourth LL edge. Again, this can also happen for corners. If you trace all four and they do not form a valid OLL configuration, you know you made a mistake. You might find that no matter how often you retrace LL, you do not get a correct OLL -thus prompting you to look for errors in F2L (once more, I won't aid you in recovery, but I'll tell you I've done it successfully): Without the fourth piece you would and could not have noticed
• There is also that little detail of permutation parity that works in you favor, but not enough. Three corners and two edges are enough to ascertain the location of every piece, but you still won't know the orientations of those two edges. Vice-versa for three edges and two corners, too.
• No matter how many you trace, you at least know you've made an error if two pieces land in the same spot at the same point in the solve.

If you trace the corners, you will get (in clockwise order from UFL):
OLL locations of the traced UFL (WRG), ULB (WGO), UBR (WOB), and URF (WBR) corners

Ignoring order temporarily, you can use the orientations to carefully build up an image of the OLL.

If you know your OLL (unlike me, for complicated reasons), you will easily recall that this is the nice Sune-like alg on the right.
So, you can recognize the OLL, trace each piece -without orientation, because that gets fixed- through the OLL (and remember their order) and go on to PLL. Or, you can use compound OLL.

If you don't know OLL, you can split this into the standard EOLL (with FRUR'U'F' or FURU'R'F') + COLL. However, I highly recommend using compound OLL instead. It does EOLL and COLL together in one look, and does not move many pieces. It is not difficult, and a lot faster and more accurate.
In fact, even if you are comfortable with all of OLL, compound OLL will often actually be be faster and more accurate than tracing around 8 stickers.
I would only use a regular OLL alg (if I knew it) if it is considerably faster than compound OLL, and tracing will be very quick & easy (for example #1, I would have used the OLL if I had known it then).
If you're going for speed execution, regular OLL is probably best, though, but only if you have the time and can trace accurately.

In example#2, I avoided EOLL, so it's just one three cycle. The edge ordering remains unscathed, and the corner ordering is only shifted by a three-cycle.