Here are some problems to help you get started. However, these can only take you so far. If you are ready to go to the next level see USACO Coaching.

Beginner

Intermediate

Advanced

Learn coding syntax to write your first program!
(USACO Bronze and Codeforces Div 2 A/B Curriculum)

If you can write simple programs (using tools like loops), learn algorithms and data structures.
(USACO Silver/Gold and Codeforces Div 2 B/C/D Curriculum)

Once you know all the standard algorithms and data structures, apply them to hard problems to score higher in programming competitions.
(USACO Platinum and Codeforces Div 2 D/E , Div 1 D curriculum)