How does losing an electron result in a positive charge?

A proton has a positive charge, an electron has a negative charge. Usually, the amount of electrons and protons is the same, but when an electron is lost usually because of radiation or a chemical reaction the resulting amount of electrons/ protons results in a different charge for the atom in general.
When there are more electrons the result it a negative ion, and when there are more protons it is a positive ion. 
So, to answer your question: if an electron is lost from a neutral atom and there are more protons than electrons you get a positive charge. Have a good day!