You see, that's the thing with carbon steel. While it gets super sharp, keeps an edge well and is a relative breeze to sharpen, leave it in contact with water or anything acidic and it isn't a gentle patina that will develop but rather ugly, destructive rust. I want to hold my hands up here, it happens to the best of us and, after whipping up a storm in the kitchen, it is all too easy to put off the clean down at the expense of your knives.
The pictures above are a couple of sorry looking specimens that didn't get the best care. However, a bit of TLC later they are back to new. I have experimented variously with Barkeeper's friend, rust erasers, different grades of wet and dry sandpaper and wire wool. It depends to a degree on the grade of the rust, the finish of the knife and quite how f&*cked it is to which works best and there are up sides and downsides to both. Bar keeper's friend removes some of the patina alongside the rust, whereas if you have a mirror finish you don't want to go near it with a rust eraser.
In short, don't panic. Rust can generally be removed without affecting the performance of the knife. Nip it in the bud early on before it pits the surface and be extra careful of any rust around where the blade joins the handle as, believe you me, you don't want a rusty tang. Once you have got rid of it, don't do it again. Keep a teatowel at hand to wipe the blade after anything acidic, don't leave it submerged in the sink or damp (a quick wash of the blade and then fully dry), and if it is humid or you aren't using it for a while, a coating of food-safe oil is your friend.
Simples. Don't let the fear of rust put you off carbon steel.