If you're old enough to remember the fall of the Berlin Wall, then you probably remember your dad shaving with a hefty Gillette double-edge razor (often called a "DE" razor). Gillette doesn't make those any longer, but you can purchase an excellent Merkur double-edge razor for about $40. Pair this with a quality badger hair shaving brush, quality English shave lather, and a little patience and you may find yourself with the closest shave you've ever had. I recently decided to switch from my usual Gillette Fusion ProGlide and give the DE a try for a week. I was very pleased with the results. So you can try it for yourself, I'll fill you in on the tools and techniques I used.
To get the best shave, you'll want to shave after a hot shower. This will help soften the beard and make shaving easier. Because the traditional wet shave with a double edge razor takes a bit longer than shaving with a modern cartridge razor, I recommend shaving at the sink rather than in the shower. This will allow you to clearly see what you're doing and filling the sink with a few inches of hot water will save gallons versus shaving in the shower.