The answer will depend on what information you do have: one of the base angles, the base and one of the legs, the base and one of the base angles. There are also other possible combinations involving medians, etc.
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First find 180 minus the vertex angle and divide that by 2 to get the other angles. Then solve the other sides by using sin(vertex angle)/base=sin(other angles)/other sides.
You will also need the angles so that you can use the Isosceles Triangle Theorems to solve for the base of isosceles triangle when only two sides are given.
It depends on the infoamtion that you have.
If its angles are 45, 45 and 90 degrees then it is an isosceles right angle triangle and its properties can be worked out using Pythagoras' theorem and trigonometry
If its angles are 45, 45 and 90 degrees then it is an isosceles right angle triangle and its properties can be worked out using Pythagoras' theorem and trigonometry