How do you know when to resign?

I recently had someone resign after 10 moves, normally I would not want to quit that early, how much down in material should you admit defeat?

It's not how much material I'm down. It's when I no longer have the will to play on. When my ego has been crushed and I want to escape the torture of seeing my dreams of victory (or at least drawing) shattered.

I'd resign when my position is bad enough that I feel that a draw is impossible to achieve. When material is going to be lost, you need to try and maximize your compensation (material and other positional considerations) and counterplay. If you can gain enough counterplay (A great attack, shutting down your opponents activity, etc.), you should have enough compensation to draw or win the game.

You know when to resign when something more important than that game comes up. It could be after one move, it could be after a hundred. Knowing when to resign has nothing to do with how many pieces you have on the board.

When you see your opponent is playing a forced sequence that leads to a mate or   to a position in which you have no chances to even draw

+1

The problem is that many chess players (especially beginners) are not skilled enough to see when they are already lost; I think this is what the original poster is asking about. The short answer is "whenever you feel like the game is lost for you." A beginner might not resign until losing many points of material, or seeing an unstoppable mate in 2 or something. A stronger chess player may resign over a lost piece and a GM may resign over just a pawn lost without compensation. This makes sense because a GM versus another GM probably won't comeback from a lost edge (even if slight), but a beginner versus a beginner has many chances for each side to blunder, so playing on against them is logical. 

Sometimes when I'm losing I play some 'testing' moves to see if my opponent knows how to convert the position to a win; if they demonstrate that they know what I am looking for, then I resign then and there. If they are shuffling or playing inaccurate moves, whoo, I love it; you can bet I'm going to begin my comeback from a losing position into a win!

When you have a turtle head popping out.

When your wife yells, "Are you still playing that game? We were supposed to leave 20 mins ago."

When you're sitting in the family's church pew and your priest clears his throat and looks you dead in the eye.

When your cat jumps onto the computer desk demanding to be loved and it steps on your mouse causing you to blunder.

When you set the oven timer for 30 mins an hour and a half ago and the fire dept is beating on your door cause black smoke is rolling out your kitchen window.

It depends on the board. If your down a piece and 10 moves later, your opponent forces you to lose another piece, it's highly unlikely your opponent will blunder the game away, or launch a risky attack.

Been there, done that! 🤣

I'd resign when I know for a fact I would win if the board was flipped.

When your position is lost and your opponent has enough time to mate you. 

White to move. Would you resign as White in these position?

last one no all the rest yes

None of those

You can resign when your position is "hopeless" and you cannot foresee yourself recovering from it. (There are some exceptions, e.g. it is nice to allow your opponent a pretty checkmate)

Never resign in bullet.

well i never give up! even at expert level, there are mistakes to be made...

 i mentioned some in my top 3 swindles blog post

one of those games i won when i was going to get mated in 2 but he blundered a rook with check instead

The lower the skill level, the more likely chance of coming back in a lost position. For higher level players, being down a piece is already resignable.