First, a high-level roadmap.
Watch the Princeton Coursera course on algorithms (by Robert Sedgewick), mostly up until Dijkstra’s algorithm and not much more than that. Try to follow along and code as you go. You don’t need to implement things in Java unless you already know Java.
Read The Algorithm Design Manual for general algorithms and data structures background. Go through most of it. (You can skip the giant appendix about specific algorithmic topics).
Buy Cracking the Coding Interview. We’ll be using this as a repository of coding problems and solutions.
If you’re working on an algorithms problem (such as out of CTCI) and can’t figure it out, spend no more than 20-30 minutes without making progress. Just go look up the answer. Contrary to popular belief, most struggling past 30 minutes is pointless.
Some people will disagree with this. [NW: Like Tom and Chris Uga.]
Screw those people.
That said, if you find up having to look up the answer to more than 2/3rds of problems, your problem set is too hard and you need to downgrade.
But banging your head against a wall or staring blankly at code is a waste of time. For code/algorithms problems, you very much want to maximize the density of learning per hour.
Any time you look up the answer to a coding problem, try to understand the solution. Walk through it with a debugger if it’s particularly mysterious. Read multiple explanations of why it works.
Then—and this is extremely important—if you didn’t solve the problem completely on your own, treat the problem as though you never solved it at all. Put it back into your rotation of problems. Mark it as something you need to try again from scratch. Wait at least a day, and try to solve it fresh. If you fail, rinse and repeat ad infinitum.
And finally, structure the hell out of your learning. Make a schedule. Know exactly when you’re going to be working on this stuff, when you’re going to take breaks, when you’re going to go to lunch, etc. Build flexibility into your schedule, but have clear goals for how many hours a day you’ll spend studying.