P2P Guide

P2P can be described as Peer 2 Peer, sort of like a phone call to one person. You request the file from that user and that user responds and allows you to download that request, very like the ringing of a phone and the answer of the phone. Here is a simple little diagram below, of a phone call and how similar it is to P2P.

You dial the number => You hear the phone ring => The recipient hears their phone ring => They answer the call.
Now P2P is very similar as you will see.
You request file XYZ off user => You see the client "Handshaking" => The user recieves request for file => User allows transfer.

As you see it is very similar i used a phone as an example.
Hopefully this description helps you, if not look below for a google definition.

Google Definition

P2P
Peer-to-peer: Electronic file swapping systems that allow users to share files, computing capabilities, networks, bandwidth and storage.

Alternative Definition

P2P : A method of file sharing over a network in which individual computers are linked via the Internet or a private network to share programs/files, often illegally. Users download files directly from other users' computers, rather than from a central server.

P2P has evolved a lot since the early days of Napster, this was the first real world wide known P2P client, until the RIAA and MPAA decided to sue Napster and close them down.
"You may close Napster down, but you will never stop what they started"

Now there are thousands of clients all fighting for this Domination that Napster did have, a recent example is the program called KaZaA, now KaZaA was the first client to use decentralised servers to host the files, meaning they only provided a search and the program, not the files where as Napster held all the files on a server for everyone to download. KaZaA was a good client with the introduction of Sig2Dat links. These links were VERIFIED links, this ment that you used this HASH link and you could download that link exactly as it said. An example of this is say you wanted Microsoft Word(For Trial USE,I DO NOT CONDONE PIRACY) you could use a hash index site and download that HASH link, then KaZaA would interperate this link and search the network for this file and download it, but the file wouldn't be fake, it would be a genuine file, with no virus's or mislabling. Very smart for the time of P2P, it was groundbreaking. (A further description of Sig2Dat can be found HERE)

Now this link is a standard link throughout the whole P2P world, but not Sig2Dat links anymore, the popular ones are ed2k,magnets,arlink and bittorrent.
There are many advancements with the Hash links of these files, making it easier to find and download these files for TRIAL use, or if its a free program, for general use. The use of these Hash links are very popular with different groups as it defines a standard for each P2P client which most people abide by. Also with the spread of VIRUS's and Spyware the use of these Hash links are more popular.

Examples of these sites are:
Google - I dont condone piracy so search for the sites yourself. Sorry.

The Networks

There are various networks on the internet now. Back in the day the FASTTRACK Network was the most popular, but then the RIAA and MPAA decended on this and flooded the network with fakes and started suing people.
Now its different there are many networks and the networks which im releated to are G2, G1, Ed2k, Bittorrent and Direct Connect.

G1 - Gnutella 1
G2 - Gnutella 2
Ed2k - Edonnkey Network
Bittorrent (BT) - Bit Torrent Network
Direct Connect (DC) - Direct Connect Network

These are the best networks at the moment and seem to be very good at quality and speed, with the execption of Edonkey as its slow as anything all the time.
At the moment i currently have installed:
Shareaza - For the G2, G1 and Ed2k networks ( it also handles BT links and Piolet Links)
Azureus - For my BitTorrent downloads ( More stable for BT than Shareaza as its a dedicated client)
DC++ - For the Direct Connect, this network provides a "Hub" with many users sharing files which allows chatting and social areas.

The reason i use 3 clients is because of the choice i have on each network.
The G1, G2 networks are great for any type of files and can provide very fast speeds, this network sometimes has rare files but Ed2k is the main network for rare files.
The Edonnkey network is great for finding files fast with lots of sources, but downloading is slow and based in queues taking longer to download files.
BitTorrent provides a very large range of files, the advantage of BT is the speed and the mass of files avaliable on the network is unknown but it is very good for rare files, if you can find the correct sites.
Direct Connect allows lots of hubs to get faster downloads, a direct connection allows for good downloads and sometimes multisourcing, this network is good for files which are popular and you even find the rare stuff on these hubs and lots of different contents.

Hopefully these guides help you chose the best clients suited for you, but i recommend you have the same clients as they are very stable and widely known with the proper P2P communities.