You've been given the general overview as to how things are done but I wanted to hit on a few things because of how important they are.
1. CONTRACTS -- Always Have One Not Matter Who You Work For! I've had clients that I've worked for, for years and the one time I let things ride on a handshake and not paper, I get screwed. . . the client had the audacity to laugh at me as she said (to my face) "you should have had a contract".
2. DOWN PAYMENT -- ALWAYS HAVE ONE -- I suggest that you go with a 30% NON-REFUNDABLE deposit as a minimum and with newer clients, especially commercial, a 50% deposit is wise. The reason is simple; with such a large deposit at stake chances are quite strong they will not change dates on you unless absolutely necessary (which is a flexible thing) and this includes, canceling on you. To that latter point, it prevents them from discovering someone that offers a comparable service at a much lower price and bumping you out of the deal so they can contract the less experienced schmuck.
3.) Final Payment -- Always to Be Paid Prior to the Show -- the reason is very simple; many club owners (particularly) will have you come in, do the night and then forget to pay you after the fact. This is a classic course of action no matter the kind of act you may do, musicians are constantly screwed when it comes to this sort of thing. Same goes with Birthday Party gigs however. The only exception I have when it comes to this rule is when I'm working with a major corporation, such as when I worked with Ford Motors; I allowed them to do the standard 30-day net styled payment. This is something that I've only had problems with once, when I worked for a major company out of Paris. It took me six months to cash their check. From that point out I insisted on an American Bank drawn check for the agreed upon sum whenever I worked with any company not based in the U.S.
4.) Invoice/Copy -- ALWAYS KEEP A HARD COPY -- Computers crash, digital formats for saving data change. I have tons of material I can no longer retrieve for years back, because it is on a floppy disc of one form or another. Having that digital copy is awesome and convenient, but as I've said, things become obsolete and being able to pull up files from a decade or two back, a hassle. . . unless you fork out the bucks to have that data transferred to the new version of the same old thing . . . which you'll have to do again the next times Microsoft decides to change their shorts on a whim. And let's not discuss Cloud technology; I simply don't trust it and seriously suspect that "they" will eventually put thumb screws on us when it comes to having access to our own data. There's just too many variables in that scenario to make me comfy. That leaves us with keeping hard copy on everything. When files get too big or dated, you box them and put them in storage or even transfer them to Microfilm, an easily scanned and retrieval system that is still in use by major corporations and governments. It's easily stored in relatively small space and remains a legal accounting source of "proof" . . . but I honestly doubt anyone here will ever need to consider such an alternative, not even Copperfield needs to take things that far.
File Cabinets & Hard Copy may seem old fashioned, but they tend to have much longer life expectancy over technology.
4.) Insurance & Riders -- While you should have your own insurance on prop replacement and liability your contract, especially when it comes to working large events in which you equipment will sit over night, possibly over several nights, you should require the client to cover your costs as well. This includes added insurance requisites when you employ livestock, in particular large exotics like Tigers & Elephants but similarly, large farm animals. There is always an insurance requisite when it comes to such things in that bunnies bite and scratch as to parrots. . . you must cover bases.
Riders can cover a great number of things but the key issue you need to address is privacy when it comes to dressing areas, and small prop security. This can be everything form a bedroom in someone's home to a private restroom space on the low end to formal dressing rooms and "green" areas. Riders can cover many other things but this is something that really needs to be weighed.
6.) Thank You Cards -- The Forgotten Must Do -- Always, no matter what kind of gig it was, always send a thank you card to the booker if one is involved, as well as the client. If you're working a hotel or banquet hall you've never worked in the past, send them a note of thanks as well, praising the help staff, food quality, etc. and how they helped make for a pleasurable and fun event.
This may sound peculiar and even a "waste" of time & money, but expressing good thoughts and appreciation is the quickest way to generate business as well as a reputation for being "one of the good guys". So always send out appreciation cards within 72 hours of the gig and don't be chency; send nice cards that reflect a sense of quality. They are after all, a reflection on you and the kind of person you see yourself as being. . . which brings us to another important issue. . .
Your Letter-Head & Envelopes, everything you use in your press materials and correspondence, should NOT be "stock". Have everything you print and send to a client, on quality paper. You may want to have pre-printed stationary with raised ink, embossing, etc. your printer can be set so as to allow proper room for this addition. Again, it might seem like a lot of work and such a "little thing" but it's just such little things people will remember most . . . especially the people that make the big decisions when it comes to hiring the right act for certain events.
Invoices can be Black & White, but you still want to use decent quality paper to print to so that it shows how much you care about the little things.
These are standards that a handful of older magic texts explain when it comes to the business side of things. We don't hear too much about it now days but those that are familiar with it can testify as to its strength.