You'll need to use several methods to solve each side and angle of the triangles. The first thing I'd recommend you do is Find each angle. We know that interior angles of a triangle all add up to 180. So, look at the triangle to the left. There are two angles given, 56 and 110 degrees = 166 degrees. Subtract 166 from 180 to get 14; angle C is 14 degrees.
Since angle C is next to the other angle beside it, you can add them together when looking at the whole triangle (all three combined). So, the lower left corner of the large triangle is 34 degrees.
From here you'll need to use simple trigonometric functions to find the lengths of the sides. You would do this the same way you'd solve a problem where you find the height of a tree (given one angle and the length of one side).
Other than this, you may need to use the law of sines to find a few others. Law of sines is simple but takes a long time to explain, so I won't get into it. Also remember that the three angles in the middle will all equal 360 in the end, so if you know two of them, you can find the other by adding those two and subtracting from 360.