Find all connected 2-sheeted covering spaces of $S^1 \lor S^1$ This is exercise 1.3.10 in Hatcher's book "Algebraic Topology".

Find all the connected 2-sheeted and 3-sheeted covering spaces of $X=S^1 \lor S^1$, up to isomorphism of covering spaces without basepoints.

I need some start-help with this. I know there is a bijection between the subgroups of index $n$ of  $\pi_1(X) \approx \mathbb{Z} *\mathbb{Z}$ and the n-sheeted covering spaces, but I don't see how this can help me find the covering spaces (preferably draw them). From the pictures earlier in the book, it seems like all the solutions are wedge products of circles (perhaps with some orientations?).
So the question is: How should I think when I approach this problem? Should I think geometrically, group-theoretically, a combination of both? Small hints are appreciated.
NOTE: This is for an assignment, so please don't give away the solution. I'd like small hints or some rules on how to approach problems like this one. Thanks!

As far as I know that one way to do this is to write the representation of the group that you have here which is  then act by this group on the set {1,2} by taking a= (1), a=(12) . Then this will give you all possible covering spaces connected and disconnected. I hope that is correct and helpful for you. 
