My son is a big HP fan and asked for a HP birthday party. After some internet research on those party idea sites, this is how we did it (sorry for the bad pics):
The theme was the first book, Harry Potter and the Sourcerer's/Philosopher's Stone.
Rooms in our apartment were decorated as places from the book, and we roughly followed the plot of the first days in Hogwarts.
As invitations, the kids got the classic invitation letter (green ink on brown packing paper that I burnt on the edges, Hogwarts crest printed on envelopes, seal from melted wax crayon and rubber stamp). I even persuaded some moms to put it on her kid's pillow and tell him an owl brought it in
When the kids arrived, we parents greeted them in teacher's costumes (Dumbledore and McGonnagle) and lead them through the hidden entrance between the platforms (our door) and told them that they would now be equipped with everything a wizard needs on Hogwarts.
Then the kids were led to Diagon Alley (slightly out of order of events, but that was okay with the kids), which only opened after I tapped the secret sequence at the grey fabric that hid the door. Diagon Alley was the kids' room and decorated to contain two shops: Olivander's Wands and Madam Malkin's Robes.
My other son volunteered to be the wand maker. His shop had a counter with several wands on it, and a christmas garland that works with batteries and a on/off switch. So now we told the kids that they would have to test the wands to find out which one was the right one. The wands had been made in advance by my kids following this tutorial on instructables
Technically, if a kid had the right wand, Mr Olivander was supposed to secretly turn on the garland, so it would seem like done by the wizard and his wand. Well... birthday kid takes his favourite wand and wields it confidently, and his brother decides to add some suspense and NOT light the garland. "Not the right wand for you. You need to try another one."
Tears of shock (the usual party meltdown part one), and we insisted he needed to test THAT one again, only concentrate some more. His brother also agreed on a second test that he previously had declared to be too silly: If a wizard wielded the right wand, Mr Olivander would be hexed to speak in animal's noises. That dried the tears alright.
Mr Olivander's shop was very popular, and lighting the garland by wand and make Mr Olivander bark like a dog was played for days...
After everyone had their wands, they got their robes. For this, I had found some soft and cheap black fleece online and cut it into Hobbit half cloaks after this pattern
without making the hood. It's shorter than the usual Hogwarts robe, but the width of the fabric was perfect for a half cloak and I figured the kids would move easier in it than in a full length cloak (although the same pattern can make longer cloaks too). I hightly recommend that cloak, it's really only cut out, no sewing involved, and looked so cute.
The cloaks closed with simple safety pins, and some kids snatched some leftover fleece and some more safety pins and improvised themselves inside pockets for their wands. Genius!
After that, we went into the living-room that had been decorated as one half Great Hall, and the other half class room.
The Great Hall was decorated in House colors (crepe paper streamers) and House Crests that I had printed on foto paper. We then sorted the kids into their houses. We had experimented with putting a cell phone into a hat for the talking part, but it didn't come out so well, and so we just threw some house pins into a big hat, and let the kids draw one. The pins were foto paper on brooche pins. They held well for several days, and I could also make more house crests on demand.
Now the wizards were fully equipped. (There's a tutorial for the little pointed hats on instructables which would have looked cute too.) Their wizard equipment was also the party favours and cost me less than 5 Euros per kid.
It was time for Dumbledore's speech and the banquet. We had a cake with candles, and yellow muffins with paper wings that were supposed to be snitches. The wings had been made by my son, too. He's not into papercrafst usually, but cutting and pasting the wings on toothpicks was something he loved. We also had some little pumpkins as decoration and pumpkin juice (cooked squash with ananas and orange juice - the kids didn't really like it, but I did). Also, I had some gummi bats and some all flavor Bertie Bott's beans on the table as decoration.
Then, the kids learned their first spell: Lumos. The candles on the birthday cake were that kind of prank candles that always light themselves again when they are blown out. So I let them blow out the candles, wield their wands, say "Lumos" and everyone was able to light the candles like this. The boys were fascinated no end and practised until the candles were burnt down
After the cake, we went to the class room (just a space we had cleared and decorated in House colors). I gave them some magic classes. Potions was the most popular one because it made the biggest mess
It was basically some beetroot juice (when we ran out of it, I had some cherry juice that worked just as well) that was treated with liquid soap, fancy named vinegar (first change of color), then with soda powder (another change of color) and finally citric acid, which reacted with the soda and made the whole potion foam out of the beaker. I had given each kid an emtpy glass and a transparent plastic container (so we could all see the color changes well) that stood on a towel (provide enough of those...), and I had filled the ingredients in scientific or fancy looking bottles and labelled them with names like troll snot, powdered unicorn hooves and the like. Before the whole mess started to foam all over the container, I told the kids that this would show us who of them had a big secret. So everyone wanted to know who had the biggest secret. Potions class was such a succes that we had to do it again (note: provide generous amounts of ingredients so you're not forced to come up with stuff like using the vinegar out of the fruit fly trap and lable it "Egyptian flea mummies out of a pyramid"
Among that many potions, we were able to produce a big range of color changes. If you want to do this kind of potions, it's a good idea to try it beforehand to get a feeling for ingredients and measurements.
Another very popular class was Care of Magical Creatures. This was good to calm down the kids somewhat. We sat in a circle, and everyone borrowed a stuffie from our kids. Then we took turns to tell us how our magical creatures was called, what it's magical properties were, what it ate etc.
There were some more classes, and after that, the kids played by themselves, and in the end, when it turned out to be too cold outside to take them out for Astronomy class and show them stars like Sirius and Bellatrix, or constellations like Draco and Scorpius, we decided to watch into the beginning of the movie as not all kids knew it already (yes such kids exist).
This was our most favourite birthday party so far. There are many more ideas one can include (too bad we couldn't play Quidditch!). The budget for the party didn't have to be huge as I only bought fleece, crepe paper, and the candles and candies, I had everything else in my stash already. There is no end of great stuff online for this kind of parties. I would have loved to make chocolate cauldrons... HP snacks... something crafty with the kids... more classes (they were over faster than I thought and the kids were still asking for more), more games... but in the end, the compromise of time, preparations, and space made for a great birthday.
On a side note: not all kids knew the Harry Potter book or movie (something to keep in mind), but all kids were into wizards, and loved to have a wand and do spells, take magical classes, eat muffins and try awful Bertie Bott's beans. Also, it was a birthday that didn't include the contests and games we usually do, so no stress with the competitive kids