A while ago I looked into the chemistry and science of shaving and changed how I go about it, for the better.
Hair, like fingernails, softens when wet, so I always shave after a shower, and the first thing I do in the shower is soak my beard. I then use a pre-shave preparation and scrub with my fingernails around the throat area to tease up any potential ingrowers. When finished I don't dry my face, but go straight to the sink to shave, using shave gel and a Gilette Fusion Mach 3.
I used to shave any old time of day and the results always led to irritation, which I put down to sensitive skin. Now I rarely get any issues. A sharp blade helps.
If I take a soak in the tub I can shave without any soap at all - the stubble is so soft and the skin lubricated with perspiration. However, I find that a small amount of soap does help show where you have and haven't yet shaved.