If you do something economically, you do it in an efficient manner. Acting economically wastes no money or effort.
Though variations of this word often relate to the economy — the financial system — to be economical also means to be thrifty in other senses. For example, if you do your homework economically, you do it quickly and correctly, without wasted energy or time. If you run errands economically, you take the shortest route and don't get sidetracked. If you take a road trip economically, you drive across the country as fast as possible and in a straightforward manner, without deviations.