Depending on what you are trying to do,is this a one time deal or are you going to make a bunch?
What the other folks have told you about classes of fits is correct,but,for example,if what you really want is a 1 in round bar pressed into a bored hole in a plate,it may be good to find out what tooling your machine shop has.
Some machining processes give better dimensional control than others.
A press fit is a fairly narrow tolerance range,likely less than .001 on a 1 in press(I'm not looking it up)
So,if the best you have is boring the hole on a Bridgeport with a boring head,you can get pretty close with good tools,but working to less than .001 is like shooting sub MOA groups,it depends on a lot of things and you get a flier once in a while.
Now,if he has a hone machine,the hole can be held very close,in the tenths,so you would have good control over the hole,and if you bought 1 in drill rod with a ground OD,for example,you would hone the hole to fit the drill rod,or,a 1 in dowel pin.
Sometimes a machinist has better control over the diameter of the round bar,so it may be best to bore the hole first and fit the bar to the hole.
It might work best to let the man know what you need,like,a press fit,and let him figure out how to get there with what he has.