Peaches, a 2013 $10.00 * note is worth...........Drum Roll , please..............................exactly $10.00 !! UNLESS, the bill is in CU (Crisp Uncirculated) condition, which means it must be in absolutely perfect condition, then offer it on eBay (those guys will buy anything) and you may get $11 or $12 dollars. Remember, condition is everything, also, the older the bill (at least pre-1970) the value could go up. Also consecutive serial numbers, say, if you had 5 of those, in CU condition with consecutive serial numbers, THEN you'd have something a currency collector might be interested in. Personally, I have 9 $5 * notes in absolutely CU condition, so uncirculated that you can still feel the embossing of the serial numbers. I estimate the 9 bills, together, to be worth about $90 - $100.00 or just about double their face value. Separately, only about $5 -$6 each. The key to the value of those is the 9 consecutive together, and of course the condition. If you're watching your bills, keep watching for the stars, they come in all denominations, but watch for different color seals. You're probably only seeing green seals right now, but watch for red, blue, yellow and brown seals. Good Luck and welcome to Coin Talk....where we talk about......you guessed it.....COINS !!!
The dollar bill is worth only a dollar. Typically, serial numbers only matter if they're consecutive or if you're playing Liar's Poker. You could watch the serial numbers for misaligned numbers or extra thick ink on the numbers, but those things are so common and inconsequential that there is very little, if any, upgrade to the value. Other, more experienced members can certainly provide more, or better, advice.
If you decide to try to sell anything on ebay, just remember that you must figure in your cost and all of the fees associated with it and PayPal or you could be paying for someone to take that off your hands. Post some photos of it here as well!