Tecumsah
Some of the service records for the Royal Navy are online, part of DocumentsOnline
www.nationalarchives.gov.uk/documentsonline/Records of men who joined from 1873 onwards are all online, some of those who joined 1853-1872 are also online (the rest are being added). So it's worth having a quick look to see if he's there before you go. If he is there, don't spend £3.50 downloading it, wait until you get to Kew and you can see it there free of charge (it will only cost 20 to print it out).
If he's not there, you will have to look at the microfilm at Kew - pretty straightforward to do, there are neat little 'how to' leaflets in the searchroom, and the staff can help you out if you get stuck.
There are other records you could look at, such as ships' musters and log books, depending on what you find in the service record. As this will be your first visit, make sure you take two forms of ID with you (one with a signature, one with proof of address), to get a Readers' Ticket which you will need if you want to look at original documents (you won't need one for the service record, which will either be online on on microfilm).
Have a great day, and don't be overwhelmed by the size of the place. You won't be the only beginner, and you can get very nice coffee and cake in the cafe when it all gets too much!
Good luck
Mean_genie