I get some of the worst in grown hairs known to woman. From experience, I once learned to shave against the grain in order to get a closer shave for various things like smoother legs or face. Ultimately, as it turns out, there are better techniques that do not involve shaving against the grain. The problem is hairs get trapped under the skin. To avoid doing this, avoid shaving against the grain.
My technique is to run a wet hand against the grain to get the hairs standing up. At this point, shave with the grain or at an angle if necessary. Repeat this until it looks smooth. If necessary, to get closer, stretch the skin AGAINST the grain and hold it while shaving WITH the grain on the stretched area. This seems to work really well on my face as well, providing the same smoothness as against the grain without the ingrown hairs for me. The key is you need to be very careful about applying this uniformly, and over time the skin will become healthier, smoother, and easier to shave.