I guess the process will take different legnths of time depending on a: what tests they need to do and b: if you need any specific treatment and c; your health authority.
I can remember being in exactly your shoes, so worried about what they are going to say, preparing yourself for the worst, and in my case, I think that the stress of not getting pregnant straight away was what was stopping me getting pregnant. I had an irregular cycle and after trying for a while and getting nowhere, i started having bleeds in between and everything, so it is no wonder I didn't get pregnant - it was heartbreaking every month though, so I know how you are feeling.
My initial appointment was in April, I had my laparoscopy in July, got the results in September and had a bouncing baby boy the following 5th July. Our friends were going through the same as us at the same time, but had started investigations a bit earlier, they ended up having IVF and had a girl 10 months after our first boy. I had a second son 13 months after my first!
I guess that if you are ovulating and your partner has a good sperm count, then as long as the egg and the sperm can meet then it looks positive. If you do have a blockage, I think that that is precisely the situation that they will be able to help with.
I think that it is 1 in 4 couples have problems conceiving, so you are not alone - just keep your chin up. My sister in law tried for 9 years and now has 2 beautiful children through IVF and a work colleague tried for 12 years with all sorts of treatments, but conceived naturally after they had really given up and has a lovely baby girl.
I am sure that you will be fine - just be careful that you don't put too much of a strain on your relationship, they will warn you about that at the clinic probably.