Wash your skin with soap and water. This is not to get it clean, although it does that, but to break the surface tension. It's like when you shampoo: the first application doesn't foam much, but the second foams like crazy. Breaking surface tension allows the hair and the skin to get wetter.
Apply your favorite lather and shave, stroking the way the hair grows. Rinse.
Lather again and shave again, stroking the opposite direction. Careful, there is no drag at all and it's easy to take off a layer of skin. Rinse and dry.
This simple trick makes a razor last so long you will forget when you got it. However, it works best if you have soft water. If your water is hard, consider using bottled water for shaving. Don't snivel about the cost of new razors. They are cheap, and you are getting maximum value for money with this method. Get a new razor to start and replace it occasionally.
About the lather: it's not very important. I shaved for years using the same product I used to wash my dishes. A steamed towel works ok, too.
If backwashing doesn't work (eg on December 1st when I'm removing the moustache), I have an old toothbrush that I clean it with between strokes. I never reuse a razor - combination of tough bristle and sensitive skin, sometimes the blade gets nicked on first use and I get cut.
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