How would I get a character's model from a Player?

The character model as in the one in workspace, and the Player as in the object in Players

You could have easily found this on the wiki. Every Player has a property that's equal to their character, or nil if it's not loaded yet.

player.Character:BreakJoints()

player.Character

That's it. However, you do have to wait for the character to load sometimes. Here's getting the character from a LocalScript,

local player = game.Players.LocalPlayer
local character = player.Character or player.CharacterAdded:wait()--methood for waiting for character to load.

You can simuarly get the player from the character. Here's a script from a simple touch brick,

script.Parent.Touched:connect(function(part)
    if not part.Parent:FindFirstChild("Humanoid") then return end--checks if what touched the brick is a character or npc.
    local player = game.Players:GetPlayerDromCharacter(part.Parent)
end)

Your question was simple so my answer will be simple. Good Luck.