First: Make sure you have the minimum stat requirements for your class and role. These can be found out by talking to your class leader. Without the minimum you will not receive an invite.

Second: Have consumables. Always. It's always a good idea to bring consumables that will increase the raid's chance of success. For those who raid frequentely these can be found in the guild bank. Otherwise these can be collected, found in the AH, or crafted.

Third: Ensure you have the necessary addons. We like to experience encounters as they were meant. However, sometimes certain addons are necessary to be successful. Omen threat meters, Deadly Boss mods, and Big Wigs are all required. There are several other encounter specific addons that are useful but not required.

Fourth: Sign up for the raid you would like to attend before the due date.

Fifth: Be online and on time when raid invites go out. Make sure your gear is repaired and you know the fights.

There are a few ways to increase the chances you'll be able to sign up for a raid or attend one. 

First: Establish yourself on the blog. Being known increases your chances of being liked...making it more likely you'll be invited.

Second: When you go to a raid perform your best and don't QQ.