Using a safety razor puts you in control and going from a multi-blade cartridge to a safety razor is like switching from an automatic car to a manual gear change - you get better performance by being more in control, but you must learn how to use it, practice your technique, and pay attention to what’s going on.
The first issue is pressure, with the safety razor, you must not use pressure to try to get a closer shave, in other words don't try to remove growth in one pass of the razor.
Pressure must be light with the razor and the blade doing the work - exerting additional pressure will only cause problems (cuts, razor burn, etc.). As described below, you obtain a closer shave with more passes, not more pressure.
The key is progressive stubble reduction over multiple passes, often two, generally three, and sometimes even four.
After pressure, the key variable in using the safety razor is blade angle. Try putting the head of the razor against your cheek, the handle perpendicular to the cheek and parallel to the floor. Gradually bring the handle down toward the face as you make a shaving stroke, pulling the handle to drag the head down your cheek.
When the handle’s dropped around 30º from the initial perpendicular (depending on the razor you’re using), the blade will make contact with the whiskers and begin to cut as you pull the razor. That’s the angle (more or less).
The idea is that the edge of the blade is cutting through the whiskers, not scraping over them. If the room is quiet, you can hear the sound of the razor cutting through the whiskers. The idea is that you use the razor like a scythe, not like a hoe.
As the skin on your face curves - over the jawline, around the chin, and so on, you continue to adjust the razor’s position to keep the blade close to parallel on the skin being shaved.
Using short strokes enables you to focus on blade angle (and pressure) for the entire stroke; in addition, for a short stroke the angle is likely to be constant. It helps to lock fingers and wrist, moving the razor with your arm: this makes it easier to maintain a constant angle.
The right cutting angle is different for different razors. You’ll have to experiment to find the right cutting angle for each of your razors.
In summary, proper technique with the safety razor consists of using light pressure and the correct blade angle over your entire beard area, including the neck.
When you can master this (and it only takes a week or so to get great results, you'll really enjoy shaving and will probably never want to go back to a disposable or semi-disposable (Mach3, Fusion and the likes).
If you are really interested in wet shaving and getting the best from your razor, you may like to read the great book by Michael Ham - 'Leisureguy's Guide to Gourmet Shaving' from which much of the text above was kindly provided. You can buy the book here >> .