With SQL traces I was able to analyze them with Database Engine Tuning Advisor to obtain basic recommendations for perf. tuning(missing indexes, statistics,...).
Now, with SQL 2012 and Extended Events, how can I do something similar?
Unfortunately you cannot do this with Extended events unless the data from XE can be converted into the format that DTA uses or can be stored in the tables generated by DTA.
Not recommended though but Trace is is still available, so can be used if you want.
You can even use DMV's for finding missing indexes, etc.
Also worth mentioning Aaron's post : Don't just blindly create those "missing" indexes!, since you are using DTA for analysis.
To elaborate on @Kin correct answer, as far as I can tell you can still use Database Tuning Advisor with SQL Server 2012. Even with this, I wouldn't recommend blindly accepting all of its recommendations. You'd need to know your system and your workloads.
Having said that, it looks like a trace is not the only way to generate recommendations. You can use a set of scripted T-SQL statements (that hopefully reflect your workload) and you can also use the events in your plan cache.
Extended Events are more for monitoring and troubleshooting specific problems on the server. It is technically the replacement for traces, but as workloads become increasingly complex, I don't think it's particularly viable to base all tuning enhancements off of the DTA's recommendation.