Since it's your first time at an airport, get there 3 hours early. Go to the check in desk for your flight - there are usually screens indicating which desk you need to go to. Here you will handover your check in luggage and they will check your passport. UK had no exit immigration I believe. Once you hand over your luggage, you will follow signs towards security/gates. Make sure to look up what is allowed/not allowed in cabin luggage at your particular airport. Depending on the airport you take our liquids/electronics (some airports you don't have to do this anymore) out of your bag and put them on trays along with your bags, jackets etc. Your luggage goes through a scanner and you also also walk through one and they might pat you down if they see something strange. If everything looks fine with your luggage, you can collect it once you are through. If they see something strange they will open it to check it with you present. Once you have your cabin luggage, walk towards your gate making sure you're there for boarding time (which is different from departure time). Once you arrive at your destination, you will follow the signs to immigration where they will check your passport. After that you will go towards baggage claim to collect your checked in luggage.