By the definition of similar polygons, triangle ABC ~ triangle DEF (the symbol "~" means similar) if and only if the following are true:

Just as there are shorter ways than the definition to prove that triangles are congruent, there are ways to prove triangles are similar without knowing the measures of all the sides and angles.  Here is a list of them:

-AA Similarity Postulate:     If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.
-SAS Similarity Theorem:    If an angle of one triangle is equal to an angle of a second triangle, and if the lengths of the sides
                                          including these angles are proportional, then the triangles are similar.
-SSS Similarity Theorem:    If the lengths of the sides of one trianlge are proportional to the lengths of the sides of a second
                                          triangle, then the triangles are similar.
-By Congruency
-If similar to the same triangle

Here are a couple links to similar triangles:
Angle Worksheet
Homework