You asked

How do I keep the cost of my child's first communion down?

It's important to realise that while you want your child to have a special day that he or she will never forget, it's not necessary to spend a fortune. Dresses and boy's outfits can actually be purchased at reasonable prices with many high-street shops offering good quality outfits at affordable prices.
The shoes will only be worn once, so on this one occasion hand me downs are fine, If a sibling, relative or friend has a pair gathering dust in the back of their wardrobe why not make use of them? Alternatively you could try auctions online or have a scout about the shops for a cost-friendly pair.
Tiaras and veils can also be and added expense so why not use a tiara or veil that was used for a friends wedding? It's also a good idea to check high street shops for hair accessories as they will be considerably cheaper than buying in an expensive boutique.
Overstyled hair and elaborate up-style hair dos have the potential to look a little ridiculous. Why not cut costs and style your child's hair yourself?
It's also definitely not necessary to book your child in for a spray tan, she doesn't need it!
Drive your child to the Church, horse-drawn carriages and stretched limos are costly and going way over board.

Remember, you don't have to splash out because other parents are doing it.

When it comes to giving gifts to other children, €5 is more than enough to give to an eight year old child. Don't feel that you have to give money to every child in the class either, it's not necessary. If you wish, speak to the other parents before hand and explain that you won't be partaking in this. 
It's also important to realise that the day is a celebration for your child. Bearing this in mind, would your child rather spend their day in the pub or hotel or would they rather visit the zoo or a fair?
Another great way to cut costs is to get together with the other parents in advance and book a room in the hotel for the class to have a party. Sharing the cost of this will be a lot more cost effective than booking a function room for the family.

If your child kicks up a fuss about what every other child in the class is getting, remind them about the Sacrament and the true meaning of the day.

More questions

There are lots of ways that parents can cut down on expenses on their child's big day.
Preparing a party for your child's first holy communion doesn't need to cost the earth
Catering for your child's communion or confirmation party can be a daunting affair but with plenty of planning it needn't be.
If you're looking for a traditional Holy Communion gift then there are lots of options to choose from.