When I made pathfinding it was based on a manually built nodegraph. It implemented something much like the algorithm Zack0Wack0 linked there, except mine went through the whole nodegrid keeping a list of the nodes it had been through for each iteration (to try to prevent infinite loops, they still occurred though) and the total distance.
The function calls itself at the new node with the current path recursively, though it had a whole bunch of schedule-and-callback shenanigans so the bot would enter a "thinking" state where it would begin pathfinding, and upon completion make a callback which pushes the path onto the bot and starts its movement.
So, borrowing the first frame of the Djikstra's algorithm runtime image from Wikipedia there:
Bot is at node 1, connected to 2, 3, and 6
Call function on nodes 2, 3 and 6:
findPath(bot,2,"1",7)
*not ideal path, not documenting*
findPath(bot,3,"1",9)
Node 3, visited 1, distance 9
Check connected nodes 1, 4, 6
Visited 1, skip
findPath(bot,4,"1 3",20)
Node 4, visited 1, 3, distance 20
Check connected nodes 2, 3, 5
5 is target node, distance 6 for total 26 - return "26 3 4 5"
findPath(bot,6,"1 3",11)
Node 6, visited 1, 3, distance 11
Check connected nodes 1, 3, 5
5 is target node, distance 9 for total 20 - return "20 3 6 5"
findPath(bot,6,"1",14)
*not ideal path, not documenting*
Return distances of 26 and 20, 20 is lower so take path sent with 20 "3 6 5" - go to node 3
On reach node 3, go to node 6
On reach node 6, go to node 5
On reach node 5, call destination reached callback
Obviously this can get quite long hence all the schedule shenanigans, scheduling 10ms for every node, so a path to the destination with 5 nodes will literally return faster than a longer path as well (and then all the other "thinking" schedules are cancelled)
And also obviously, bots aren't always going to be standing right at a node - bots search for the nearest node to their location that they can raycast to, then begin the pathfinding process from that node while they walk there. You could also use four more raycasts to check a 'bounding' area of the bot from their current location to the node and see if it's really clear to walk, after doing a basic check so you do one raycast per non-feasible node and five total per potentially feasible node.
However, creating a pathfinder that will literally find paths on its own is more or less impossible - well, perfectly possible I guess, if you don't mind it freezing your game for several minutes while it pathfinds.
However you can always just set up a nodegrid for your bot deathmatchers or whatever.
