Daily Astronomy is an e-mail service that sends out daily astronomy problems (and solutions). The problems are divided in three levels (Beginner, Intermediate and Advanced), and you can choose from three plans:
Free - one problem per day (for free);
Starter - one solved problem per day (€ 2,99/mo.);
Pro - 3 solved problems per day, one from each level (€ 6,99/mo.).
The problems and solutions are sent directly to your e-mail inbox.
The beginner problems are comparable, in difficuly, to the school and regional selections; the intermediate to the national selection, and the advanced to the international competitions and beyond.
If you have just started studying astronomy, I suggest choosing the beginner level first, changing to intermediate only when you feel comfortable solving beginner problems in all the proposed topics.
If you can comfortably solve all problems from the regional phase and want to train for the national, I suggest choosing the intermediate level, switching to the advanced level from time to time, for instance on a day when you have more spare time to think about a problem.
Finally, I would suggest choosing the advanced level if you can easily solve most problems from the national phase, and are training for the international competition.
Remember that you can change level and unsubscribe whenever you want, by following the instructions at the end of every e-mail you receive.
I have also formed a group of talended students in Physics and Astronomy who have previously represented their contries and were awarded medals in several international olympiads, such as the IAO, IOAA and IPhO. If you'd like to get in touch with one of us for private tutoring, write a short email to firstname.lastname@example.org, introducing yourself (age, country, your level of knowledge).
Daily, consistent practice is the best way to get good at problem solving. In this field, it is a lifelong skill whether you are a student or a professor.