If you want to do it yourself, most grocery stores will rent you a carpet cleaning machine. My advice is don't use too much cleaning solution- if you do, your carpets will look great for a few weeks, and then crud will start sticking to the soapy residue and you're back where you started.
Yes, rentals of carpet cleaning machines are quite readily available. Check first to verify if the advertised price includes a jug of the soap or not, as it usually does not. Purchasing the soap will be an additional cost to the rental.
Also, if you are renting the machine for 1 day, try to get it the day before a holiday, or a day when the store in closed, because then you will not have to return the machine until the Next day.
We have always rented them from a local grocery store and have had to buy the soap, it is what is recommended for that particular unit. Just follow the directions This way we do not have to store or maintain the machine.
You can rent them at Walmart and Home Depot, too!