How is Elastic Net used?

I would point you towards this blog post: http://www.datarobot.com/blog/regularized-linear-regression-with-scikit-learn/.

The documentation is lacking. I created a new issue to improve it. As Andreas said the best resource is probably ESL II freely available online as PDF.

To automatically tune the value of alpha it is indeed possible to use ElasticNetCV which will spare redundant computation as apposed to using GridSearchCV in the ElasticNet class for tuning alpha. In complement, you can use a regular GridSearchCV for finding the optimal value of rho. See the docstring of ElasticNetCV fore more details.

As for Lasso vs ElasticNet, ElasticNet will tend to select more variables hence lead to larger models (also more expensive to train) but also be more accurate in general. In particular Lasso is very sensitive to correlation between features and might select randomly one out of 2 very correlated informative features while ElasticNet will be more likely to select both which should lead to a more stable model (in terms of generalization ability so new samples).