Like the Pile cast, the Wiggle cast can be used when casting to a fish that is rising directly downstream of you, it is simply a slightly different technique.
At the end of your forward stroke and after the stop, simply Wiggle your rod tip from side to side, the size of the wiggles you need to create will be dictated by the speed of flow you are faced with, and the basic rule is the bigger the wiggles in your fly line, the longer they will take to straighten out, so if you have a fast downstream current to overcome, it is no good making very small wiggles as they will be straightened out very quickly by the flow and will not afford your fly much time to act naturally before drag is once again an issue. If you have a slow downstream flow to overcome, it can also be a problem if you have created very big wiggles, as your target fish may often take your fly whilst still having lots of slack line in your presentation and this can also become an issue. Gauge the size of wiggles you think will be relevant to the speed of flow for a successful outcome.
An alternative way to the above method of creating your wiggles is to make uniformed circles directly in front of you after the rod tip stops in the forward cast, this will also give you neat wiggles of line on the water downstream of you, either large or small, dependant on the size of circles you create with your rod tip at the time.
Strangely enough, you will also find that by moving your rod tip up and down after the stop in the forward cast you can also create wiggles of fly line on the water, so experiment with all of these methods and it won't be too long before you are proficient with them all and they are assisting you with catching more fish.
So when would we need a Wiggle cast as apposed to a Pile cast?
A wiggle cast works great when casting onto a downstream current and yes you can make the wiggles any size you want them to be to combat the differing speeds of flow, but what if your downstream path is hampered by very close overhanging branches? That's when your Pile cast comes into it's own, as you can set the Pile cast off from much higher upstream than the wiggle cast, simply allowing it extend underneath the branches as it drifts downstream.
The disadvantage of both of these casts is that you will have slack line to contend with if a fish takes (unless it takes at the end of the drift). "Hey I think we can suffer that for the chance of a fish that we may have missed out on anyway".