In all honesty, in most cases I believe a person can reasonably pass for the other sex assuming a few things. First of all, if a guy wants to pass as a woman, I suspect having a beard/mustache is a really bad idea.
After that, it's a matter of finding the clothing you feel comfortable wearing. Remember, many women are beautiful and many are just plain ugly. But, 99% of women are just plain women. That gives a guy a lot of latitude in how he presents himself as his feminine better half. Now, if you're 6'5" and 270 lbs. it may be difficult to pull off; but, again assuming a more normal height and weight, I believe it's only a matter of trial and error, practice, and maybe professional instruction with regard to makeup. For a woman wanting to look like a man, I believe it is a lot easier. Dress like a slob and don't concern yourself with the finer details of grooming.
That may be an over simplification; but, think about most of the men you see other than in a professional setting. You get the idea. I'm 5'8" and 195 lbs. I could never pass as a centerfold; but, with good makeup and the proper clothing I believe I could pass as a frumpy, overweight, old lady (I'm 76). After all, right now I'm a frumpy, overweight old man. Obviously, I doubt it would be easy to do in front of folks that have known you for any length of time; but, that's a given. However, if you are in unfamiliar surroundings and in the vicinity of people who have never seen you before, I believe most people would never notice. It is extremely rare that I ever even give a thought as to whether or not a person is the biological sex they present themselves to be. About the only thing I ever wonder about (and it is rare) is when seeing certain women is whether or not they might share an interest in certain mild BDSM activities I have an interest in.