You only need a wireless-capable router (and set it up properly, of course).
Basically, you plug your router into the DSL modem, like you do with your PC right now. You also have to set up your router through the admin panel so it can log into the network the same way you do with your PC right now (login data from your ISP, which you also use on your PC currently... i.e. user account and password, etc). The router then automatically connects to the internet and forms a network hub, where you can plug in multiple machines to connect to the internet via the router.
The router has some slots to plug network cables in them, like the one the modem has (where your PC is plugged in right now and the router is plugged in then instead). You can hook up your computer there, and the data is just slaved-through from the ISP to your modem through the router to your PC.
At the same time, the router also transmits the signal to form a wireless network, which isn't much different to hooking a computer up with a cable to the router, just that the connection is done via radio transceivers.
The PS3 then needs to be set up to match the routers wireless settings (same encryption protocols, i.e. WPA2)... assuming it has a wireless transceiver built in (but I think it does). You need to scan for wireless networks in your vincinity (obviously after the router has been set up) and find the network your router is transmitting (when you set up the router you can give your network a name to be able to identify it; default is usually the router's specification). Then connect to it, put in the proper keyphrase (which you hopefully set up on your router earlier, because it's a good idea to do so), and when that is done you should have both connected to the same network.
1mbit isn't great, but should be ok to play games.
Bye
Thanee