You definitely need to write some code - I don't believe you can learn any language without doing that. K&R has lots of exercises you can practice on. It's difficult to know how long in terms of elapsed time it will take to get a good working knowledge - I used to teach pretty much the whole language in 4.5 days, but that is quite intensive. I'd suggest about a month, if you are doing an hour or so a day.
Edit: I must admit, I find it a bit depressing that so many people think C is so difficult. K&R is 272 pages long, in my copy, and covers basically everything you need to know, including the standard library. Is there book in ANY other programming language that covers the whole shebang so concisely? I don't think so, and the reason is not that K&R is compressed in some way (Brian Kernighan is THE greatest techical writer, IMHO) but that the language is simple and easy to describe.