Before sending out the invitations you will need to think carefully about how many children to invite.
When children are very young this can be a vexed question. Often they have not yet got to the point where they have an established friendship group, and many parents feel that it is safer to simply ask the whole class. This can seem like an easy solution, but might mean laying on entertainment for as many as 30 kids, which is a very tall order.
If you can elicit a list of favoured friends from your child, this is the best option. But bear in mind that a list of friends that includes virtually everyone is the class, with just three or four exceptions, is a poisoned chalice. In that instance, you should try and bargain your child down to a more realistic number, or bite the bullet and suggest inviting everyone. You wouldn't want the three or four children who aren't on the list to feel miserable and rejected.
Send out proper invitations, don't rely on word-of-mouth. This doesn't need to be expensive; you can buy ready-made invitations to kids' parties (with blanks you fill in). Or you can have fun designing your own invitations on the pc - perhaps including a photograph or some wacky typography.
When your children are young it's best not to entrust the invitations to their care. All too often you'll find a bundle of battered envelopes at the bottom of their school bag just days before the party. A better option is to hand out the invitations yourself at the school gates.
Whatever the type of party you have chosen, you will want to have a good idea of the number of children involved (and some venues will need exact numbers). You should therefore put RSVP on your invitations.
There is an unfortunate tendency amongst parents not to be very assiduous about replying to children's invitations. All too often, they rely on word of mouth, and trust the children to communicate with each other. This is totally unacceptable.
When their child is invited to a party parents should always reply promptly (ie within 3-4 days) to the invitation. This does not have to be a formal process - a quick phone call or word at the school gate will suffice.
If you are organising a party and find that you are suffering from a distinct lack of replies as the big day approaches, you have no alternative but to ring round, or track down the errant parents at the school gate. Explain that you need to know numbers in advance, and indicate that provisional acceptances ("James may be able to come, but I'll have to check with his grandmother to see if she can pick him up…") are not good enough.