I wont go into the whole - "my husband isn't really keen" thing - you yourself know what is right. I do however have relevant experience of the fertility clinic.
Has your husband been to the doctor at all?
If not, it is likely that they will physically examine his equipment and conduct a series of sperm tests - usually he will get a bottle to fill at home and he must then deliver it to where it needs to go - most likely the clinic - as soon as possible while keeping it at body temperature - my husband tucked his into his armpit underneath his jacket, but then he was riding a motorbike!
They will have a talk with both of you about the frequency of se and about your relationship in general - trying for a baby can be very stressful and can result in a lot of relationship breakdown.
They will then want to carry out an investigation on you - this can vary in content depending on the results of previous tests - personally mine consisted of being weighed, measured, blood test and blood pressure and an internal scan.
As a result of the initial tests, I had to go for a laparoscopy and something else that the name escapes me, where they flush dye through your tubes and check that they are working correctly.
I was then told that I had one partially blocked tube but that it shouldn't prevent me form concieving - I got pregnant the next month after two years of trying.
tbc