If you want to get rid of mice but don't want to use inhumane traps or messy poisons, make your own humane mouse traps, with materials you probably have around the house. A humane mouse trap simply catches the mice and places them in a holding container, so you can take them to another location and set them free. Get some tasty bait and make your own humane traps.
A bottle trap is a good way to capture the mouse and release it again without having to touch it, ideal for those who are a little squeamish. Cut the top off a 2-litre bottle so that you make an opening large enough for a mouse to get through. Place the bait in the bottom of the bottle, and lay the bottle on the edge of a counter, chair or stack of books. Weight the bottle down on the front end resting on the high surface by taping coins or some other weight so that it just barely keeps the bottle in place. Position a box under the bottle. When the mouse goes in for the bait, it will upset the balance and the bottle will topple into the box, where you can take it to release it.
A balancing trap using a stir stick and a buffet pan is effective, especially when put on a flat surface, like a concrete floor in a basement. Just smear some peanut butter on the end of a wooden paint stir stick, or similar flat wooden stick. Place that end of the stick on the floor, and then use the other end to balance one side of the buffet pan in the air. It looks precarious, because it is. The aim is for the mouse to come along, start chewing on the end with the peanut butter and knock the other end out of place, bringing down the buffet pan to create a trap. You simply need to scoop the mouse into a pail and release back into the wild.
This is another good option if you're hoping to never touch the micet during the trapping process. For this method, you'll need an empty garbage can and some newspaper. Secure the newspaper tightly over the mouth of the dustbin so that it looks taut and sealed. With a knife, cut a very small "X" about 5 cm by 5 cm (2 inches by 2 inches) in the exact centre of the newspaper. Dab a little bit of peanut butter, or another bait on the corners of the "X" shape. When the mouse goes after the bait, it will fall through the "X" into the garbage can, where it will stay until you can release it.