It is unlikely that you will have to deal with paying taxes for your stay in Peru. If you submit the paperwork to register as a foreign resident then you should click here to find out updated information about paying income taxes in Peru as a foreign resident.
When you register as a foreign resident and receive your Carnet de Extranjeria then you will need to pay a small yearly fee as a foreigner living in Peru. Click here for more information on paying the annual $20 foreign resident fee. Part of having a Carnet de Extranjeria will also be the fee to renew it each year. On the date of the anniversary of your Carnet, you need to pay a fee to renew it. Click here for more information on paying this fee.
The benefits of the Carnet are not having to worry about renewing your tourist visa and you get perks like free entrance into some ruins and other sites as a resident of Peru.
If you are only moving to Peru for a briefer period, one or two years, and do not plan on registering as a foreign resident and receiving a Carnet, then you will not be subject to these tax regulations. You will have to plan on traveling outside the country and re-entering every 3 months, however, in order to renew your tourist visa.
If you are living in an apartment or house that doesn't cover water and electricity as part of the rent, then you'll have to pay these bills yourself. It's normally not too big of a hassle, so don't stress. Like in most countries, the water and electricity bill are monthly bills.
You should have the receipt delivered to your house. You may find it slipped under your door or tucked into any metalwork on your door. Your bill will tell you how much water or electricity you've consumed in the past month and should compare this with previous months. The bill will also tell you when you have to pay by.
You can find small stalls inside corner stores that process bill payment in most busy areas of your city. Don't wait till the last day to pay! Everyone else will as well and the lines can sometimes be long.