$\displaystyle {v_{1}, v_{2}, v_{3} } $ is a basis for a three dimensional real vector space V. Show that the set $\displaystyle {v_{1} + v_{2} , v_{2} + v_{3}, v_{3}+ v_{1} } $ is also a basis for V.

I am finding it really hard ot understand the concept of finding bases, and my notes dont make sense, am not even sure where to start, do i first find a spanning set ?