They should be 'skin tight' and certainly wont feel in any way like normal street shoes so standing around in them or walking round the house as you would to test a standard shoe are not the correct methods to confirm the fit.
It is extremely common for your first pair of rockshoes to feel extremely strange and far less than comfy, after all they are a specialist shoe for a specialist task and just as a ballet dancer has notoriously uncomfy 'shoes' to dance in, us climbers have to suffer a little for our sport too.
Basically, there should be absolutely no gap between your toes and the end of the shoe but your toes should not be curled up excessively or painfully. Your toes should also be squeezed laterally (again, not painfully) in order to allow you to put as much power through the big toe as possible with your other toes providing additional support while you are climbing.
It should not be possible to pull off the shoes once they are tightened and conversely you should have to loosen the laces (or velcro straps) in order to put them on. Having to use the two finger loops on the back to pull the heel on is a good sign that the fit is not too loose.
As you climb more regularly your foot strength will improve (rapidly) and you'll find them more and more comfy as time goes on.
If made of leather or unlined, they will stretch about 1/2 - 3/4 size and will soften up slightly with use so bear this in mind too when assessing the fit - just as with street shoes it's nearly impossible to get that well-loved velvety feeling from a brand new pair of shoes until they have been worn and used for a few hours. The extra performance you will get from a good pair of climbing shoes will far outweigh the discomfort and you'll soon forget you have them on once you're on a good route !
