Can I get a Lulav and an Etrog to use on the holiday?
Yes. A Lulav and Etrog can be ordered through your supply chain (NSN 9925-01-488-9309, listed as four species) or at no charge from the Aleph Institute. http://www.aleph-institute.org/
Can I get time off to attend services?
Yes. While training and operational commitments always have priority, your Chain of Command will be willing to work with you provided that you talk with them well in advance. Make sure you speak with your Chain of Command AND fill out a special request chit (or whatever your particular command requires), remembering that the earlier you anticipate this need, the more likely you are to get the time off.
Can I build a Sukka on base?
Yes. If you are married and living in base housing, it is a good idea to talk to the housing office before putting one up in your yard to let them know what you are doing and to make sure you know that it is a temporary structure. If you are living in the Barracks, talk with your unit Chaplain and work with your Chain of Command to find an appropriate location. Please keep in mind that most Jewish communities aboard base will build a communal Sukka somewhere that is there for your use as well.
Can I build a Sukka aboard Ship?
Yes. Rambam Hilkhot Sukka Chapter 4 Section 6 makes it clear that a Sukka built aboard a ship is Kosher. Check with your Chaplain several weeks to two months before the holiday to make them aware of the requirement and so that they have time to help you find an appropriate location and to help you get the appropriate materials.
What is the smallest a Sukka is allowed to be?
A Sukka only needs to be big enough for most of one person to fit inside for a long enough time to make Kiddish.
What if I am unable to build or locate a Sukka?
Jewish Tradition teaches us that the Sukka is a reminder to construct a Jewish space for us to use for 8 days. While a Sukka is always the best option during the holiday, try to do something different for your meals during the Holiday (eat outside, make plans to eat with the other Jews in your unit etc).
What if I have other questions?
Talk to your Chaplain and ask any questions you have. If s/he is unsure of the answer, they can put you in touch with any of the Rabbis serving with the Navy to help you figure out the answer to your questions.