I wouldn't say it's 'very' messy but it will certainly make a difference over time.
I have always tanned in one room of the house but my carpets throughout the house, my woodwork, surfaces etc have discoloured over time and I do have decorators in yearly.
I have now set up in my bathroom, had my bath taken out and a shower/spray tan area installed and got myself an extractor unit & ensure that I leave the door closed and the fan on for a couple of hours once I've finished working
My advice would be to get the fan from the word go, keep your spray gun low and if you can't get rid of the carpet make sure it's well protected with dust sheets, clean your wood work etc after each day.. Mine all had a lovely green tinge to it but since this years lot of decorating I've gone OCD in keeping it white!