Do the division and write your remainder over the original denominator. Simplify the fraction if possible. 

For example, converting $\frac{21}{9}$ into a mixed numeral, you ask yourself "how many times does 9 go into 21?", it goes in twice (since $2\times 9=18$ but $3\times 9=27$), with a remainder of 3 (since $21-18=3$). So we can write our answer as $2\frac{3}{9}$ (which actually means $2+\frac{3}{9}$). But notice we can simplify the fraction, so we should rewrite our answer as $2\frac{1}{3}$.

Note: we could have cancelled common factors at the beginning. 

Multiply the whole number and the denominator, add the numerator, and put it all over the denominator.

For example $2\frac{3}{4}$ can be written as $\frac{2\times 4+3}{4}$ that is, $\frac{11}{4}$.

To understand why, realise that $2\frac{3}{4}$ is shorthand for $2+\frac{3}{4}$ and if we want to add these numbers we need to have a common denominator (recall the denominator of a whole number is 1). Our working could look like this:

$$2\tfrac{3}{4}=2+\frac{3}{4}=\frac{2\times 4}{4}+\frac{3}{4}=\frac{2\times 4+3}{4}=\frac{11}{4}$$

but in practice we normally don't write anything more than $$2\tfrac{3}{4}=\frac{2\times 4+3}{4}=\frac{11}{4}$$