It will be a full check. You wont find (well you shouldnt) any optometrists that dont do a full check.
so what will happen?
You will go into the room with the optometrist and sit in a chair that everyone thinks looks like a dentist's (it doesnt as there is no spit ball or sharp instruments). He/She will ask you what your symptoms are, a bit about your eye history, your family history, your medical history etc.
Then you will usually read the eye chart with each eye seperately. Sometimes if it is really hard to see they may give you a pinhole to look through as well.
Sometimes they may do other tests at this point to check how your eyes work together and other things. sometimes not.
They may then "measure" the power of your eyes using a light and various lenses, or they may put you on a machine that does this (or sometimes they just "guess" the starting point). THis measurement basically gives us a starting point and should improve your vision quite a bit if it was bad to begin. They will then refine it with your input (does this look better or does this one etc). Dont worry there are no right or wrong answers and it is TOTALLY OK to say "I cant tell, they look the same to me) After all that they should get a fair idea of what prescription (if any) you need to see well.
Next they will go on to check the health of your eye. This could involve all or some of the following.
Looking at the front of your eye with a type of microscope, looking inside your eye with a lens or a handheld torch type of thing, measuring the pressure in your eye with either something that puffs in your eye or something that rests gently on the front of your eye (after you have had drops in to numbit of course). Sometimes you may need drops to makeyour pupils (black part) bigger so they canget a better look inside your eye. Some optometrists are starting to do this as standard (but I would be suprised if that is included in a $60 test). If they have trouble seeing inside or see something that they want a better look at you amy be asked to come back and have the drops put in.
After all that they should explain whether or not you need glasses, why you do, whether your eyes are healthy etc.
Basically thats the main points but they may throw in some other tricks as you go along. It all depends on what your probs are and what they find out along the way.
Just going off what you have written, you probably are a little bit longsighted and that means you see better far away than up close but it also means your eyes work too hard to see things and tend to get tired easily. Working up close or at a computer makes them feel worse and go blurry. You will probably get glasses that are reasonably weak but that just take the strain off your eyes. There may be no problem at all and it could just be that you need to take more breaks, change your work station around etc.
$60 is a pretty standard price, in fact its a little on the cheaper side (without being budget of course). My practice charged $65 and I have heard of much higherand as low as $45 (usually where there is HEAPS of competition).
Hope that helps, sorry its a bit long winded and I am quite pleased I can remember what goes on

I have to go back to work on Saturday
PM me with where you are going if you like and I may be able to give you the inside scoop.