Roll for Shoes doesn't really have a "combat system" as such — unless you houserule one in, of course. Rather, combat in RfS is basically handled using the same general mechanics as everything else: the player rolls Nd6, where N is the level of the skill they're using, and tries to beat the GM's roll.
The thing to keep in mind is that RfS is a rules-light and narrative-heavy system. That is, you don't roll to deal X hit points of damage to enemy Y — you roll to do something (charge at an enemy waving your sword, toss a rock past their head to distract them, shout insults at them to make them angry, etc.), and use the roll to see how well the attempt succeeds, and thus to influence how the GM will narrate the subsequent events. This might involve things like, say, penalties on later rolls due to injury or fear or distraction, or simply some of the combatants deciding that discretion is the better part of valor, and running away.
All this should happen at a fairly high level. While you can certainly have lengthy combat scenes in RfS (say, a massive bar fight, an assault on an enemy stronghold, a fencing match or a long chase after fleeing enemies), it's quite possible for a simple one-on-one combat to only take one or two actions. It all depends on how much detail you and your players want to get into.
Since a single example may sometimes be more useful than pages of description, here's an example combat scene loosely inspired by a game I ran some time ago:
GM: OK, so Timmy runs through the woods in the direction of Sally's voice. Stumbling out of the bushes, he sees the clearing and the tree Sally has climbed into. The werecat-thingy is crouched under the tree, snarling at Sally as she continues to belt it with pinecones, but turns to face Timmy as it sees and hears him.
Timmy's player: I wanna save Sally, so I guess I'll attack.
GM: OK, the werecat is facing you with its fangs bared, hissing. Those claws look sharp, too. How are you going to attack it?
Timmy: Can I roll to see if I have a weapon? Maybe a knife, or just a stick?
GM: Sure. Roll 1d6. (Timmy rolls 1; GM rolls 5.) Um... OK, you don't have a knife. I'm pretty sure the camp instructors wouldn't let you play with knives unsupervised, anyway. You do find some used chewing gum in your pocket, but you're not sure how that would help you.
Timmy: Aw, that sucks. Oh well, I've still got my Brute Strength (2), so I guess I'll just try to punch the cat thingy on the nose.
GM: OK, you charge straight at the werecat and try to punch it with all of your 9-year-old muscles. The werecat is pretty agile, though, so I'm gonna roll 2d6 too. (Timmy rolls 6+1; GM rolls 3+5.) Well, your punch is good, but the werecat is faster than you and just barely twists out of the way. You can feel the whiskers brush your hand, though.
Timmy: Aww, that was close. Wait, didn't I have XP from before? (GM: Yes.) Can I use one XP to upgrade my fighting skills?
GM: Sure, how's "Fists of Fury (3)" sound? (Timmy scribbles on their character sheet.) Anyway, you did manage to kind of scare the werecat with your charge. It's retreated a couple of feet up the tree trunk, and is clinging to it with its claws and still hissing at you.
Sally: I throw more pinecones at it!
GM: Sure, roll 1d6. (Sally rolls 6; GM rolls 2.) Nice. The werecat-creature's backside is just too tempting a target to ignore, as it's hanging upside down on the trunk. Your well aimed pinecone hits it right under the tail, startling it and making it let go of the trunk and land on the ground beside Timmy. Oh, and you just got a new skill, too! May I suggest "Accurate Aim (2)"?
Sally: Cool! (Scribbles on character sheet.)
Timmy: I'm just gonna try another punch with my Fists of Fury (3)!
GM: OK, you know how this works, roll for it. Actually, I'll just roll 1d6 for the werecat because Sally distracted it. (Timmy rolls 2+5+3; GM rolls 3.) Well, that one sure worked. As soon as the werecat hits the ground, you smash your fist right into its pink nose. There's a kind of a crunching sound, and you'll later notice some blood on your fingers. The first thing you notice, though, is the earshattering wail the werecat lets out as it turns and runs away into the woods, nose slowly dripping blood. Gradually, the sound fades off into the distance. Looks like it's gone, for now at least.
Timmy: Awesome! And kinda eww. But still awesome!
Ps. I started writing this answer while the title of the question still said "combat" rather than "injury". With the new title, I might've done better to pick the earlier scene, where Sally fought and got scratched by the werecat. I don't think the scratches ever ended up having any mechanical effect in the game, but they did convince the player to run away and use her character's Climb a Tree skill to retreat instead of continuing combat.