I use a good shaving oil- shave secret. The oil creates the slickest surface I've ever shaved on. Helpful for sensitive skin as you don't have to press very hard, and when you do (upper lip for me) the blade slides smoothly, rather than getting caught on whiskers.
I've always gotten my closest shaves with this oil. Keeps away the 5 o'clock shadow until the next morning.
The other benefit is the oil is clear, which makes it extremely easy to see where the hair is, and if you need another pass.
If the skin starts drying, just splash some warm water on it, reactivates the oil.
The mineral oil does not clog your pores, and leaves the face moisturized rather than dry and chapped.
Other stuff that helps is making sure you have a clean razor.
I use the razorpit. It's advertised to "sharpen" your blade, but in reality it just cleans it. Getting off any residue, and stuck hairs. I've found that it extends my razor's "useful life" by 30-40% or so.
RazorPit Men's Razor Blade Sharpener, Black
https://www.amazon.com/dp/B004W2UMDW/ref=cm_sw_r_cp_api_OiL8ybWE3A03TSHAVE SECRET SHAVING OIL- THE BEST SHAVE EVER! 18.75ML [Health and Beauty]
https://www.amazon.com/dp/B0023XF60Q/ref=cm_sw_r_cp_api_ltL8yb5NR1CAS~Brooke~