To begin your journey for Competition programming, below are some tips which would help to get into the competition programming.

Learn a programming language(like C,C++,JAVA etc) you are going to use in all competitions. C++ is predominant in programming contests and competitions because of its speed, available data structures / algorithms in STL library and because all the competitions support it.

Participation and practice is the ultimate mantra. Start with easy problems then move on complex problems and topic wise problems. Also check initial submissions of good coders and editorials, this will make you learn a lot.

Avoid time limit exceeded error, always consider worst cases before you start coding. Do proper order analysis of your solution because sometimes a little optimization is to be done but sometime there is a need of totally new and efficient algorithm.

Must learn works, proof, code and analysis of basic and well known algorithms. A book “Introduction to Algorithms”, written by Cormen, is considered Bible on this topic. Some of the well known algorithms to be worth of learning are-

Sieve of Eratosthenes, or another prime number sieve
Depth-first search
Breadth-first search
Dijkstra's algorithm
Floyd--Warshall algorithm
Either Kruskal's or Prim's algorithm
Some implementation of topological sorting, such as by using DFS
Convex hull (like Monotone Chains algorithm)
Edmonds--Karp, or another implementation of the Ford--Fulkerson method; or a preflow-push algorithm; or

Dinic's algorithm.

To get good at writing fast codes and improving your implementation follow this:

On Topcoder, start with Div2 250 master it then start with Div2 500 master it then move to Div1 250. Meanwhile keep learning algorithms and keep practicing them on SPOJ or Codechef or Codeforces . And do read the tutorials, after a time you will realize that the tricks and methods to solve are repeating themselves.

Some useful links to improve and practicing your programming abilities are given below:

https://www.codechef.com/

https://www.topcoder.com/

https://www.hackerrank.com/

http://codeforces.com/

https://coderbyte.com/

https://www.hackerearth.com/