Resources
This page contains a list of training resources.
If you are new, try this problem. It is a gentle introduction to solving your first problem from one of our previous contests.
Many of our members like the Competitive Programmer's Handbook as a broad guide. It's a very good free resource.
Other useful books include: Competitive Programming 3, The Algorithm Design Manual (a great, and informal, guide to algorithms in general), and CLRS (probably the best introduction to algorithms in terms of depth, especially good if you come from a maths background).
You can find a problem archive and judge for old ICPC questions here.
These websites host contests, and have massive archives of old problems to try: CodeForces, AtCoder, TopCoder, HackerRank, SPOJ.