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how to search mesh topology

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I'm using a winged-edge data structure to find the neighboring triangles of my mesh. However, I'm not clear on the proper order to search the topology of a mesh. Here's what I'm thinking my code would loook like. Choose a current triangle from the mesh. (loop through edges) { edge gives me 2 vertices (start, end) left traversal gives me pred and succ edge right traversal gives me pred and succ edge edge gives me 2 faces (which means one new neighboring triangle) } At this point, I've found 3 new triangles, what to do ... If I choose one, then it'll take me to it's neighbors and I haven't yet processed the neighbors of the other two triangles. Any help much appreciated.

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