To get to Avalon, you need to take a ferry from the mainland. The most popular ferry company is Catalina Express, which has departures from Long Beach, San Pedro, and Dana Point. The ferry ride takes about 1 hour each way and costs around $75-$80 round trip. Once you're in Avalon, you can walk to most of the attractions or rent a golf cart. It's also possible to rent bicycles or kayaks.
If you have more time to spend in Avalon, consider taking a snorkeling or scuba diving tour, hiking the Trans-Catalina Trail, or visiting the Wrigley Memorial & Botanical Garden. If you have less time, skip the golf course or the museum, or opt for a quick lunch at one of the many cafes around town.
Avalon does not have an airport. The closest airport is Long Beach Airport (LGB), which is about 22 miles away. Another option is Los Angeles International Airport (LAX), which is about 36 miles away. Both airports offer shuttle and taxi services to take you to the ferry terminal.