A good first step is applying the methods listed in the question Gert G linked. This covers in detail the variety of functions that can be used in different situations to cleanse input, including mysql_real_escape_string, htmlentities(), htmlspecialchars(), strip_tags() and addslashes()

A better way, whenever possible, is to avoid inserting user input directly into your database. Employ whitelist input validation: in any situation where you only have a limited range of options, choose from hard-coded values for for insertion, rather than taking the input from any client-side facing form. Basically, this means having only certain values that you accept, instead of trying to eliminate/counter evil/mal-formed/malicious input.

For example:
If you have a form with a drop down for items, do not take use the input from this dropdown for insertion. Remember that a malicious client can edit the information sent with the form's submission, even if you think they only have limited options. Instead, have the drop down refer to an index in an array in your server-side code. Then use that array to choose what to insert. This way, even if an attacker tries to send you malicious code, it never actually hits your database.

Obviously, this doesn't work for free-form applications like forums or blogs. For those, you have to fall back on the first step techniques. Still, there are a wide range of options that can be improved via whitelist input validation.

You can also use parameterized queries (aka prepared statements with bind variables) for your sql interactions wherever possible. This will tell your database server that all input is simply a value, so it mitigates a lot of the potential problems from injection attacks. In many situations, this can even cover free-form applications.