Re: ancient history help!
I assume you're talking about Rome? You should say which period, so we can give you evidence...
It's a pretty simple concept, although it's very foreign to us.
Basically in theory it was socially high (wealthy/popular/big family) patricians taking younger patricians or plebians under their wing. In early Rome, usually this would mean the patron taking on one to three clients and spending time with them.
In the later republic, I suppose from about 150ish, it became a complex relationship between one patron and anywhere from 10 to 200 clients, usually plebs. The patron would grant them favours, for example acting for them in court, arranging business prospects and employment, lending them money, etc.
From memory, the clients used to visit the patron in groups on a regular basis (I believe daily or weekly), to report in. The visits would entail the patron ensuring that everyone was acting well, although there is evidence that shows that the patrons eventually just used the visits to pay the clients (in food or money) and instruct them how to vote or how to conduct their business.
In the end of the republic and the early empire, patrons really had no contact with their clients and literally had lines of needy clients outside their houses. The patrons used to screw over the clients by pretending to help them in some big way, but were really manipulating them for political and profit reasons. The clients ended up using their patrons as dispute resolutions: Say Sam owes Joe money, but Joe says that the money is not owed. Sam would go to his patron and tell him what happened. Sam's patron would then go knock on Joe's patron's door and get it sorted out.
It became so contrived in the end, that people would literally be afraid of some peasant because he was the client of some big-wig aristocrat. Someone's client ended up becoming someone's property.
With politics, the patrons loved taking on artists. In exchange for a nice play about him, x politician (patron) would give the playwright (client) a nice bag of money. In the late republic, wannabe consuls would spend huge amounts of money in patronage, with the hopes that it would get them into office.
The thing to note is that whilst a patron could have hundreds of clients, a client could only have one patron. The system enforced a strict Roman hierachy.