Playing in Magic tournaments can be complex. Oftentimes there is no perfect answer to a given judge call. If a player ends up disagreeing with the judge's ruling, they may appeal that ruling to the Head Judge.
Note that it's not possible to appeal until you the floor judge have made a ruling. Even if you aren't sure of your call, you should make a best effort ruling.
When you first got to the match, you should have already noted the time the call started. If not, you need to do this now. You also need to note what table you are at - taking the match slip can be helpful there.
Before heading off to find a judge that will handle the appeal, make sure you understand all the details of the call. Where are you in the game? What factors lead up to this call? What points of confusion are there, if any, between the players?
Once you feel you have the facts in mind, ask the players to wait while you go get the head judge to handle the appeal.
Delivering the appeal
Appeals are potentially going to lead to time extensions, so this is a high priority issue. Walk briskly to the head judge and let them immediately know that you have an appeal. You will want to first explain your ruling and the gist of the player's appeal. As you and the head judge walk to the appealing table, explain the game state and why you made your call. Once you reach the table, you'll generally want to be silent unless asked a question. If there's some discrepancy you may want to clarify that in a friendly fashion.
Once the head judge believes they have enough information, they will then either overturn or uphold your ruling. Mark the match slip with the appropriate penalty (if any) and the time extension, and let the players play on.
This is a thing that happens
It's important to note that appeals happen. Magic is a complex game involving complex communication and complex game states. We all continue to learn and grow. If there is a useful lesson you can learn from an appeal, embrace that lesson and grow from it. If you did muff the call, you've joined the ranks of human judges: learn and grow. Know that you'll be that much better in the future now that you've gotten this particular lesson under your belt. If you need to take a quick break to get some water or briefly think, let your team lead know. After you've caught your breath, know that your EXP score has increased and you are a better judge for it.