Sorry wiley I've not made myself clear - I don't run a business myself (that's just the pipe-dream!). My DH is a self employed tradesman though, which is where my advice has come from.
From what I understand, the daycare we uses invoices at the end of the month for everybody, regardless of what services they have used. Not sure how it would work if somebody was just stuck temporarily - I think she probably would still just do all of the accounts at the end of the month.
My DH does occasionally get reluctant payers, in our experience they never, ever just say "I'm really sorry - I'm skint - can I pay half now and half next month?" Which would be fine with us. In stead they say "Oh, yeah, I'll transfer the money now..." and then don't. You ring them three days later and they say their Online banking was down, so they'll send a cheque... which bounces. My DH is sadly not very tough, and just seems to believe people. When he does eventually pull them up and threaten small claims court they pay. I would make sure you invoice properly, and put a date for payment on the invoice.
Word of mouth has been the best advertiser for us, and getting in with local businesses connected to what you're doing - so make friends with the local vets, pet shops etc! We set up a free entry on Yell.Com, but so far I don't think he's had any interest from that.
On the other hand, when I ran dog training classes I got a LOT of interest from my yell.com advert and from my own website, which I registered with google, so that when people searched for "Dog Training ", my website popped up.
Neither of us have ever paid for advertising - DH has never had a day he couldn't work, but your area is more specialised than what he does so it might not be that straightforward. I would start with everything free (or at least very cheap), like shop windows and facebook pages, and then see how it goes. Good luck!