How do I place a take profit and stop loss order at the same time and which will come first?

Depends if your broker has advanced function. For Thinkorswim you can use OCO.

I would think taking profit is when the price is above current price, while stopping loss is when the price is below current price? So if you set both, then it depends on where the future price is relative to current price. Better set a system where if one order goes thru the other is cancelled automatically. If the underlying instrument is volatile enough, you might hit both and have a short sell instead. Depends on platform.