Both good advice above.
If the client is a small business with whom you have not done business before, get paid in full prior to delivering the final product. I learned that the hard way. The client was a friend-of-a-friend, we didn't use a contract because I was dumb, and now we're using a bill collector to get the rest of our payment.
If the client is a medium-sized business, big enough that they actually have an accounting department and a formal process to pay their vendors, then it's somewhat less likely that they'll just blow you off - but it's somewhat more likely that they'll pay you on their next billing cycle after your invoice is submitted. OR, if it's a little one-off job and they don't want to jump through those hoops, your contact might just cut you a check or maybe even pay with personal credit card. Like Frank noted above, I've had it happen both ways from the same client.
There's quoting/invoicing software out there that will make it all relatively easy. My wife/boss/accountant handles all that so I don't remember what we use ... FreshBooks, I think.