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These are algorithms for the first step of the ortega method. This step involves building a single face.
I don't recommend learning every algorithm here unless you are really hardcore into the ortega method. Some of them are more useful than others. I would say that cases 1-5 are the most important. Aside from that, you might want to make sure that you know all of the algs that are 3 moves, since they are the easiest. For the rest, it can be helpful to set up the cases and then watch how the algs solve them, and this should help you learn how to intuitively solve the cases a bit mre efficiently.

This list of cases may or may not be complete, but I think it should be sufficient for just about anyone.

If the diagrams aren't obvious, here is an explanation. Each face assumes that you turn the cube to look directly at that face. The topmost part is the top face. On the middle row you have the front, right, and back faces. Finally the bottom face is depicted on the bottom. The left face is not depicted in the diagrams because it wasn't really necessary. You can see each case on a 3d cube by pasting the algorithms into the handy solver here.

You always want to start with a face that has at least two pieces already in position (you MUST be color neutral for this to work every time). Put this on the bottom side. You may need to ajust the U face in order to match the diagrams. The numbers after the algorithms are the move count, first with half-turn metric, and then with quarter-turn metric.

For each case, I have provided both the shortest solutions, as well as longer ones that may be faster to execute. Cases 1-33 have 2-gen algs available, but cases 34-50 do not (as far as I could tell).
 

1 1 FRF'R' (4,4)
R'F'UF (4,4)
R'URUR' (5,5)
RURU'R2 (5,6)
R2U'RUR (5,6)
2 2

FRU'R' (4,4)
R'F'RF (4,4)
FU'F'U'F (5,5)
F'U'F'UF2 (5,6)
F2UF'U'F' (5,6)
3 3 F'U'F (3,3)
URU'R' (4,4)
R'FRF' (4,4)
U2RU2R' (4,6)
4 4 RUR' (3,3)
5 5 UR2U'R2 (4,6)
U'F2UF2 (4,6)
6 6 RU'RU'R (5,5)
RF2R'U'R' (5,6)
R'U'RU2R' (5,6)
R'U2RU'R' (5,6)
7 7 RF2U'R2 (4,6)
R'F2UF2 (4,6)
RU2R2UR2 (5,8)
R'U2R2U'R2 (5,8)
8 8

R2F'RF (4,5)
R'FRU'R' (5,5)
UR'U'RUR' (6,6)
U2R'U2RUR' (6,8)
9 9 URU'R2 (4,5)
R2F'UF (4,5)
10 10
R'F2R2F (4,6)
RF2R2F' (4,6)
RU'R2UR' (5,6)
R'UR2U'R (5,6)
R2UR2U2R (5,8)
R2U'R2U2R' (5,8)
11 11 R'UR'UR' (5,5)
RUR'U2R (5,6)
RU2R'UR (5,6)
12 12

FU'R' (3,3)
U2RU'R2U'R' (6,8)
13 13 F2R2F' (3,5)
U'R2UR' (4,5)
R2F2R2F (4,7)
14 14 UFU'R' (4,4)
U'RU'R2U'R' (6,7)
15 15 R2UR' (3,4)
16 16 U'RU'R (4,4)
F2R'U'R' (4,5)
17 17 R2U'R (3,4)
18 18

U'F'RF (4,4)
RUFU'R' (5,5)
R'UFU'R' (5,5)
UR'U2R2U'R' (6,8)
19 19 F2R2F (3,5)
UR2U'R (4,5)
R2F2R2F' (4,7)
20 20 R'UR' (3,3)
21 21 RUR'UR' (5,5)
R'U'FRF' (5,5)
R'UR'U2R (5,6)
R'U2R'UR (5,6)
22 22 RF2UF2 (4,6)
R'F2U'R2 (4,6)
RU2R2U'R2 (5,8)
R'U2R2UR2 (5,8)
23 23 R'UR'U'R (5,5)
FU'R2F'R (5,6)
R'U'FR2F' (5,6)
R'U2FR'F' (5,6)
24 24 UR'U'R' (4,4)
R'FR'F' (4,4)
25 25 RUR2 (3,4)
26 26 U'RF'RF (5,5)
F'R2U2RF' (5,7)
R'UR2UR2 (5,7)
R'U'F2U'R2 (5,7)
R2UR'UR2 (5,7)
27 27 UR2U2R (4,6)
U'R2U2R' (4,6)
28 28 R'U'RU'R (5,5)
RU'RU2R' (5,6)
RU2RU'R' (5,6)
29 29 U'R2U'R' (4,5)
F2R2U'F' (4,6)
U2R2UR (4,6)
30 30

R'FU'R' (4,4)
R2F'U'RF (5,6)
U'RU'R2U'R2 (6,8)
U'R2U'RU'R2 (6,8)
31 31 URU2R (4,5)
U'R'U'R2 (4,5)
32 32 U2RUR (4,5)
33 33 RU'RUR' (5,5)
RU2F'UF (5,6)
34 34

UR2U'F2R (5,7)
F'UR2U'R (5,6)
F2UF2R' (4,6)
R2U'F2R (4,6)
R2F2U'F2R (5,8)
35 35

FRUF'R2 (5,6)
R'FUFR' (5,5)
R'UFUR' (5,5)
R2FR2UR2 (5,8)
R2FR2U'R2 (5,8)
R2F'R2UR2 (5,8)
R2F'R2U'R2 (5,8)
36 36

FRFR' (4,4)
FR'U2F'U (5,6)
UFRU' (4,4)
R'UR2F'U2 (5,7)
R'F'URU (5,5)
R'U'R2F'U2 (5,7)
37 37

R'U'RFU' (5,5)
RU2FR'U' (5,6)
R'U2F'RU (5,6)
38 38

U2FRU' (4,5)
FR2FU'F' (5,6)
R'F'UR2F (5,6)
39 39

F'UR'F2U (5,6)
F'R'U2RU' (5,6)
R'U'FRU' (5,5)
40 40

U2R'F'U (4,5)
41 41

FU'RF2R' (5,6)
FU2RF'U' (5,6)
UR'F'R2U (5,6)
RU2FR'U' (5,6)
U'F'UR2F (5,6)
R'UFU2F' (5,6)
42 42

FUR'F'U (5,5)
UR'U'FU2 (5,6)
UR'U'F'U2 (5,6)
RU'FR2U' (5,6)
F2RU'FU' (5,6)
43 43

F'U'RU (4,4)
U'RUF'U' (5,5)
R2U'R2U'F' (5,7)
44 44

RUFU' (4,4)
RU'R2F'U (5,6)
F'URF'R (5,5)
U'F'R2UR (5,6)
U2RFRU' (5,6)
45 45

R2U'R2F' (4,6)
46 46

F'URU (4,4)
F'RFR (4,4)
UR2F'U2 (4,6)
U'R2FU2 (4,6)
U'R2F'U2 (4,6)
47 47

FRU2FU (5,6)
R'F2URF (5,6)
R2U'R2U2F' (5,8)
48 48

FR'U2RU' (5,6)
49 49

URFR2U' (5,6)
UR'FR2U' (5,6)
F'U'RF'R (5,5)
U'R'UR2F' (5,6)
50 50

FRU'R (4,4)
F'RF'R (4,4)