The best way would be to solder them, then cover them with tape/rubber/or a cap. You can get a pretty cheap soldering iron and some solder at a craft store or radio shack that should last forever around the house.
A really good alternative is to go to radio shack and get some of the little plastic caps that you can put both loose wires in and twist together. Just be sure to get the right size for the gague of wire you are using. The look like little plastic glue lids...I think they are called wire ties.
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