Just an additional note for Windows XP installations ...
The instructions others have courteously given still lack one small item for those who have the Windows/system32 directory as the repository for the .dll files concerned with php_curl.
Go to the ext directory of your php installation and copy php_curl.dll to the Windows/system32 folder after you have followed the advise given elsewhere.
So ...
1) remove ';' from extension=php_curl.dll in php.ini
2) ensure that ssleay32.dll and libeay32.dll are in Windows/system32.
3) Copy php_curl.dll into Windows\System32 as well.
G'day
bearstate