Do you have to buy an arduino board and breadboard for every project you make? I saw something that suggested that you didn't need to, and gave me a website that led me to something that looked like some sort of all metal breadboard, but I can't find it and I don't know what it's called. Can someone help me?
No - typically, if you want to make your project more permanent, you create what is called a "standalone Arduino" - that is, you find a bootloaded ATMega168/328, put your code on it, then build a PCB (protoboard PCB, or custom etched) that has the ATMega on it, connected to just the parts for your circuit, plus the support components for the Arduino operation (resonator or crystal/caps, voltage regulator if needed, USB if needed - though most just put header pins on and attach an FTDI breakout board or cable). The "metal breadboard" you saw was probably a solderable protoboard/perfboard PCB - this is what you use. It is kinda like building your own Arduino carrier board for the ATMega (because really, that's what you are doing), but you don't need all of the extra stuff (like headers and such for wires), you just build connectors for those pieces, or solder the wires (like from sensors, switches, whatnot) onto the protoboard and hook them up to the pins on the ATMega.
Something to note, though - DO NOT SOLDER THE ATMEGA TO THE BOARD. Install it in a DIP socket; if something should happen where you need to replace the chip, it is easier to pry it from a socket than to attempt to remove it after soldering it.
Also, look for protoboards that have thru-hole plating; they're more expensive (and harder to find), but the contruction will be much sturdier than ones that just have pads. If you can't find them, then try to find ones with pads on both sides, and solder the parts from both sides; they won't be as strong, but they'll work OK. The "flimsyist" ones you will find (still, if it is the only option - and sometimes it is - use it) have pads on one side of the board only.
Hope this helps your understanding...
It's always a good idea to have some extra ATmegas on hand when you're adventuring away from the realm of the official Arduino.
You can get them all over the place, but they have to have the bootloader installed!
eBay
Modern Device
Spark Fun
etc.
course if they are extra chips with little effort you can put the bootloader on yourself using your arduino
or you can look for little kits on ebay, for like 7 bucks you can get a atmega with a bootloader programmed in, the 16mhz crystal and other passive components needed
or you can look for little kits on ebay, for like 7 bucks you can get a atmega with a bootloader programmed in, the 16mhz crystal and other passive components needed
+Shipping now, unfortunately :(. It used to be just 7 bucks free shipping, but now it's +~3-4 bucks 
Counting dollars:
A bootloader loaded chip will be 5 to 6
The lowest cost China USB/TTL converter will be 5 to 6 - (Yes, they do work!)
Additional parts (including breadboard) will be 5 to 6
A fully assembled Arduino from Hong Kong will be 19.98 (including shipping)
you should never use a metal breadboard, it will blunt your knives ;D
uh, seriously, what you call a "metal breadboard" is called protoboard, the are two main kinds: strip/veroboard that has strips of copper down it that you need to cut, or pad-per-hole board with a single pad for each hole
There are also very convenient chain-of-3 stripes!
Also there are boards that mirror the layout of solderless breadboards, which is convenient for avoiding errors when copying your stick-board set-up
The arduino philosophy is to use "shields" to avoid the purchase of many arduinos (most likely not thought-out by a clever marketing department...). For this you have to use something that fits exactly on top of the connector stripes....
Due to a mis-design, digital pins 8 to 13 are not aligned to the common 0.1 inch pitch. So some people use "prototype shields" which are not really cheap.... (So marketing comes in by the back door ;D ). Some of those prototype shields are rather awkward, some are not absolutly awkward....
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First post? Couldn't you have said something constructive or even used letters? :-/
@TchnclFl No, because he's a spamming spammer wanting to be able to post links.