There is always more than one way to do anything in Photoshop and this holds true with the converting to Black/white methods.
First off if you are looking for full tone images forget the desaturate or just converting to Grayscale. These will change the image but it will compress the tones into a muddy type image with no snap. A fast way with great results is to go to Mode, Lab color, then go to Grayscale. It will ask you if you want to discard the channels, say yes. This will drop the A / B channels and you will get a b/w with better snap. This is good for skintones and a fast fix.
The other ways are closer to the use of filters with b/w film in the good old days. Use the Channel mixer under Image. Change to monocrome and you will see the Red Channel jump to 100% and Green with Blue down to 0%. If you are working with greens like in a landscape this looks great but for people Green works better. Reduce the Red and pump up the Green till they are about 100% (for example 20% Red and 80% Green) If you want to go over 100% just a bit it will be ok. For more than just a bit reduce the Blue to equal 100% (15% Red, 110% Green, -15% Blue).
The channel mixer will give you more control but as I said Lab Color convert is fast and good.