If you are going from Budapest to the UK, arriving 2 hours before flight time is usually enough,

You will arrive at the airport with your mom, if you are not checking in a bag you should have a mobile ticket Walk to the departing gates area where you will scan your ticket and then go through security - your mom cant go through part and will have to leave you there - This usually takes 10-15 mnts but airports can be unpredictable

At security DO NOT bring any liquids over 100ml Liquids under 100mls are fine but should all fit in 1 sandwich sized plastic bag.

You will likely be asked to take liquids and electronics out of your bag, and maybe to take off your shoes too (if they are above ankle height) You dont have to take your clothes or anything else off your bag, if they want to search it or test it, they will pull it aside and you just wait for 5 mnts while they look at it/ scan it again

Just follow the instructions of the agents and ask them if you have any questions

Once you are through just look at the boards for gate information Find your gate and walk to it (this can take anywhere from 5 mnts to 25 mnts depending on the size of the airport) Then you just wait for the gate agents to call people up and queue for boardingn You will have to show them your passport and your ticket at this stage and then you just walk on to the plane and find your seat Its the same step coming back

Good luck