First, wash your face with ordinary soap and lukewarm water. Facial oils may prevent a close shave. Leave your face wet to apply what you use for shaving.
I prefer the tube gels to aerosol cans. They seem to lubricate better, and a pea sized dab covers my whole face. You get more shaves for your money from a tube gel, than from an aerosol. Gels in aerosol cans turn to foam as you apply them. Tube gels don't. One pea sized dab, rub your hands together, and apply. That should do it.
Get a good razor. Some of the newer ones like the Gillette Fusion or the Shick Hydro use cartridges that stay sharp for up to a month, and the back of the cartridge is vented so hair and residue wash clear when you rinse them. Non vented multiblade heads clog very quickly and become useless. The replacement cartridges are expensive, but they far outlast standard blades or cartridges, so you save money in the long run. Don't spend more money on gimmicky battery powered razors. They don't shave any better than the manual ones.
Shave with the grain of your beard. It not only avoids cuts, but it also avoids razor burn if you have sensitive skin.
Shave every day. Shaving one day's growth is easier, and less irritating, than shaving more than one day's.
If you do cut yourself, a small piece of toilet or facial tissue will stop bleeding as fast as a styptic pencil, and it won't sting. Styptic pencils use an astringent that stings when you apply them.
Don't forget to remove the tissue before you leave. Nothing looks dumber than a guy with tissue still attached to a shaving cut. 
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AQ 34
Your Aspie score: 104 of 200
Your neurotypical (non-autistic) score: 116 of 200
You seem to have both Aspie and neurotypical traits