First, the most economical option is Super Shuttle, which is a shared van ride for a special rate of $24 per person from LAX and $15 from Burbank Airport. The shuttle does make other stops along the way so the trip can take anywhere from 1-2 hours from LAX. From BUR the trip can range from 30-45minutes, again depending on the number of other passengers and stops.
Super Shuttle runs 24 hours a day, 7 days a week and can be caught outside any luggage claim area. Just look for the Super Shuttle Van signs and you will see a dispatcher standing nearby. Just tell him/her that you are coming to the Sheraton Universal and they will radio for the appropriate van.
Reservations are not required to come from the airport however the hotel can make them for you if you choose. Reservations are required for your return trip and can be made at the Concierge desk no later than the night before your flight.
Also, should you have a few people in your party, you can reserve an Exclusive Shuttle all to yourselves for up to 9 people for a flat rate of $95. The vans would not make any stops along the way and come directly to the hotel. These options would require advanced reservations. From BUR the cost is $70 for an Exclusive Shuttle for up to 9 people.
In order to make advanced reservations with Super Shuttle, the hotel would require the following:
-Name / number of people
-Date of Arrival
-Flight Number / Airline
Once they make your reservation, they will give you a confirmation number to give to the Shuttle Dispatcher outside the baggage claim area and he/she will radio the van.