Main advice - DON'T PANIC!
I have become quite a regular at the Lancs RO over the past year, but remember well being daunted by all that stuff to search through. I have visited a couple of other ROs and the setup is pretty well the same in all - friendly.
The whole point of the record office is, after all, to let people find the records that they need.
Check the opening times before you go. Hours can vary from day to day. The LRO open till 20:30 each tuesday, but they only open one saturday a month.
You need some ID to get yourself a reader's ticket (free), but this is usually accepted at other record offices without question. Websites will make things like this clear.
There are normally lockers to hold items you are not allowed to take in with you.
There's usually a paper index to heavily used records like parish registers. Just look up the place, and the index tells you what records are available, and the reference number under which they are filed. Most registers will be on microfilm or microfiche.
The readers for these vary from place to place, but the principles are the same wherever. Someone will be happy to show you (usually the hard part is finding the "On" switch).
County record offices usually have plenty of readers available, but some smaller places such as libraries may need a booking. The RO in Chester hold your reader's ticket hostage in return for a film reader; at the LRO you just sit down at the nearest unused one.
Associated with the reader is a placeholder, such as a block of wood. You place this in the drawer where you removed a film or fiche from. This means that if someone else is looking for that film, they know where to look, and helps you put the thing back in the right place when you have finished.
If you ask for help, staff, and even other researchers, are happy to provide it. We've all been through it in the past! I've had some excellent suggestions for documents worth looking at when I've been flagging. After a couple of visits you'll end up giving others advice!
As many have mentioned, try to be organised. I make a "to do" list, and tick things off as I do them. I also write comments like "not found" when I have searched without success, so I don't go over things yet again.
I happen to use a laptop to input and keep records. It's then only a single transcription between the document in the record office and my permanent copy. I've never had a problem taking it into the searchroom, and the Lancs RO even provide a wireless internet connection for free. I've always something to type notes on, though I still occasionally need a pencil to fill in the request slip for some document not on the open shelves.
When you find a relevant record, write down everything that might be relevant in future, such as witnesses for a marriage. You might find later that they are relatives and you will already have some idea where they were living.
Use you time for things which are difficult or impossible over the net. I can look up censuses on Ancestry from work, so am unlikely to need those when at the RO. Some records are also available at my local library, so I can get those another time.
Where there are transcripts or indexes, use them. The ease of reading a printed book rather than ancient handwriting! Someone gave up their time just to help people like you.
Use things like the IGI beforehand to prepare areas of study. There's much more on the original baptism record than the IGI, and this will usually let you figure out whether it is relevant or not.
....and if you wear them, TAKE YOUR READING GLASSES! Some of the print can be pretty small, and in older records, difficult to decipher even with them on.
