For a long time I used Jessica Fridrich's method for solving the cube. Even if you are not interested in learning speed cubing yourself, you really should read Jessica's personal history of cubing. It is fascinating, you should also watch the original master solve the cube a few times. Even with a modern explanation for solving the cube using Fridrich's method, my average time was never better than 70 seconds. I learned enough of the basic algorithms to solve the cube, but there were just too many different routines for me to master.

Gillis Roux's method for solving the cube appealed to me because there were not nearly as many different algorithms to master, and with the Roux method the solve actually becomes easier as the end approaches. I have found that Donnavan's 5 part Roux Tutorial is very helpful.

His tutorials are also available separately on YouTube.
I actually use a 7 part variation on Donnavan's version of the Roux method.
1. Left Block -- same as Roux
2. Right Block -- same as Roux
3. Corners Orientation -- top four corners (7 cases from Donnavan)
4. Corner Permutation -- top four corners (1 case from Donnavan that sometimes needs to be repeated)
5. Top -- top and bottom are all yellow and white (possibly still mixed)
6. Side -- blue/yellow and green/yellow edges -- same as Donnavan's version of the Roux
7. Middle -- same as Donnavan's version of the Roux

I have split step 3 of Donnavan's version of Roux into my steps 3 and 4. Also I have split step 5 of Donnavan's version of Roux into my steps 6 and 7.  The splitting of these two steps means that there are fewer possibilities to deal with, although, of course, since there are more steps it does slow down the solve.

Currently my average time over 10 solves is about 50 seconds. I think that with continued practice I should be able to achieve 5 seconds for each of the 7 steps. That would mean an average 35 second solve of the cube. That's not a world class solving time, but I believe that I would be quite happy with an average 35 second solve. Anyway, 35 seconds is my current goal.