44 is the international dialling code for the UK, the 00 part varies depending on which country you are calling from... i.e. from the USA it would be 01144
Normally to call any UK number (including mobiles) from abroad you dial the international access code (which is 00 in most EU countries but varies in other countries). Then enter the UK country code (which is always 44) and the UK number (omitting the leading 0).
However if you're using a UK-based mobile phone (e.g. if you've taken your Vodafone or O2 phone abroad) you shouldn't need to use ANY access codes. Just dial the usual number (or recall it from memory) exactly as you would in the UK. That's because all of your calls are routed through the UK anyway.