When you have congruent triangles, all the corresponding parts of the two triangles are the same size. Use the names of the points to help you determine which parts correspond. For example, if you know that triangle ABC is congruent to triangle XYZ, then angle A is congruent to angle X, side AB is congruent to side XY, etc.
You can also get clues from the drawings. Congruent sides and angles are often marked with tick marks (sides) and arcs (angles). Segments or angles with the same number of marks are congruent.
To solve for x and y, look at the congruent parts. Often one measure will be given as a number and the other measure given in terms of a variable. Sometimes both may be written in terms of the same variable. Setting the measures equal to each other and solving the equation gives you the value for one variable. You can use that information to find the measures of other parts and solve for the second variable, if needed.
I hope this helps.