I am a 55 year old executive who has been with the same firm for 30 yrs. I have been recently offered an early retirement package due to downsizing. I am concerned about my age and securing a new position. I know that there is age discrimination. How can I avoid this and get the job that I deserve?

Sure, some employers prefer younger guys. Some employers are also bigoted about all sorts of things, from race to religion to sex to where you play golf. If you run into this you have two choices, decide if you want to file a discrimination suit, or decide you don't want to work with people like that and get on to the next employer you do want to work with.
Pick one of these two choices and do it. I really believe most managers are more concerned about a person's ability to do the work than about anything else - and they're basically good people who will give you a fair shake.
Don't bring your fears to the interview. Tackle the problem head on and keep bringing up the fact that you can handle the job.