Fagging - Fagging is the practice of making new boys at boarding schools into slaves for the older boys. If you are fagging for an older boy you might find yourself running his bath, cleaning his shoes or performing more undesirable tasks.
Fancy - If you fancy something then it means you desire it. There are two basic forms in common use - food and people. If you fancy a cake for example it means you like the look of it and you want to eat it. If you see someone of (hopefully) the opposite sex then you might fancy them if you liked the look of them and wanted to get to know them a little better!!!
Fanny - This is the word for a woman's front bits! One doesn't normally talk about anyone's fanny as it is a bit rude. You certainly don't have a fanny pack, or smack people on their fannys - you would get arrested for that! Careful use of this word in the UK is advised!
Fanny around - I'm always telling people to stop fannying around and get on with it. It means to procrastinate. Drives me mad!
Fiddle sticks - I have an old Aunt who is much too well mannered to swear. So when the need arises for a swear word, she will substitute "fiddle sticks".
Filch - To filch is to steal or pilfer. The origin is apparently unknown.