Well, they are made out of a range of materials, too name a few,
- Early blades (nimonic alloy)
- Single crystal
the blades are casted very accurately.
these are all good at resisting heat. One resultant of the blade being subject too both high temperatures and centrifugal force is commonly known as blade 'Creep' or elongation. This is were the blade will actually stretch in its operational life, when the blade gets too a stage known as secondary creep, it extends at a constant rate, therefore, the engine modules are split and the blades are changed too avoid operational failure, which is catastrophic and will most likely destroy the engine, if its a Turbine blade.
To aviod the rotors hitting the casing, the engine has a system known as ACC, which stands for active clearance control, it maintains optimum clearance between the blade tips and the casing at all times, the blade length and casing diameter will vary as running conditions change. The casing is air cooled.
Also just too mention, the blade root known as Fir tree root is the attachment which best allows room for heat expansion whislt firmly retaining the blade, the root is the part of the blade which slots into the disk. Also bulb root design is good.
The blade itself copes with the high temperatures by a process known as film cooling, this is were compressor bleed air is fed through the blade roots or slots too cool the blade in its high temperature operating conditions, without this, the blade will melt, it is essential that the NGV's and rotors are cooled, in fact the whole assembly near enough is extensively cooled internally.
earlier blades had single pass internal cooling, now most have multi feed with internal cooling and film cooling.
I hope this helps, I noticed this topic had no replys so I thought I would say what I know !!
many kind regards