BUT HERE; we will cover the most popular/widely-used one which is TOR (who knows maybe I'll write about others like the I2P or LokiNet next)
HISTORY & ORIGIN
MECHANISM
OPERATION
(3.1) CLEARNET USE
(3.2) DARKNET USE
Developed in the mid-1990s by United-States Naval-Research Laboratory employees; Paul Syverson, David Goldschlag, Mike Reed, Roger Dingledine & Nick Mathewson to protect American-Intelligence communications online.
In 2004, the Naval Research Laboratory released the code for TOR UNDER A FREE-LICENCE & The Electronic-Frontier-Foundation aka E.F.F began funding Dingledine & Mathewson to continue its development.
In 2006; Dingledine, Mathewson, and 5 others founded The TOR Project [TOR = The Onion Router], A Massachusetts-based research-education non-profit responsible for maintaining TOR. The EFF acted as The Tor Project's fiscal sponsor in its early years.
So just in case if you were wondering if TOR can be trusted, well it's Free & Open-Source Software so you can AUDIT THE CODE yourself or get a security researcher to audit it for you & Hence, it's NEITHER a government honeypot NOR anything illegal.
(Same can't be said for a few of the websites in the TOR-Network though)
It encrypts & then randomly bounces your communications/connection through a network of relays run by volunteers around the globe.
These "ONION-ROUTERS" employ encryption in a multi-layered manner [hence the "ONION" metaphor], it will bounce your connection at least 3 times, so there are at least 3 Node-Types you need to keep in mind through which you connection will be routed through (their names are self-explaining):
--> ENTRY-NODE [Your point of entry & first TOR-Relay]
--> MIDDLE-NODE
--> EXIT-NODE [Your point of exit & final TOR-Relay & What the website sees]
None of the nodes actually know your actual computer's IP-Address [due to the triple encryption] but this also makes the network sluggish. You can also host any of those node-types (Just be EXTRA-CAREFUL while hosting an "Exit-Node" since that computer's IP is the one that's visible to the website)
Also, there are "BRIDGES" which you can use to access the TOR-Network in cases of heavy censorship;
Such as the case where you need to get around government-firewalls or don't want your ISP [AKA "Internet Service Provider"] to know you connected via TOR, in order for its users to access the open web.
TOR enables its users to surf the NORMAL Internet [AKA "Clear-Net"], chat & send instant messages anonymously [with special preparations of their own]
TOR is not meant to completely solve the issue of anonymity on the web
& TOR is not designed to completely erase tracking but instead to reduce the likelihood for sites to trace actions & data back to the user.
TOR can also provide anonymity to websites & other servers. Servers configured to receive inbound connections ONLY THROUGH TOR are called "ONION-Services" [AKA "Hidden-Services"]
That anonymity also extends to the hosting of censorship-resistant content by TOR's anonymous Onion-Service feature since they route their traffic entirely through the TOR-Network
Connection to an onion service is encrypted end-to-end & not subject to eavesdropping, An Onion-Service is accessed through its "ONION-ADDRESS"
[Denoted by a ".onion" domain similar to ".com"]