Here is a solution that uses only "elementary" operations (addition, subtraction, multiplication, and division).

>! $8 \div (3 - (8 \div 3))$ (or alternatively $\frac{8}{3 - \frac{8}{3}}$)    
>! $= 8 \div \frac{1}{3}$  
>! $= 24$  

If we allow square roots, a simpler solution is possible. 

>! $\sqrt{8 \times 8 \times 3 \times 3}$  
>! $= 8 \times 3$  
>! $= 24$ 

In fact, there are many more solutions if you allow more operations.