There have been lots of checks and captures during the first stage. Now that the king is not in danger of being harrassed anymore by all those black pieces, White can concentrate on mating. The black queen is kept under control.
5. Qb5! Qa7+ 6. Ke2! Qb6 7. Qd5+ Qb7 8. Qa5+ Qa7 9. Qb4 Qa6+ 10. Kd2! Qc8
10. - Qh6+ 11. Bf4 Qb6 12. Qe4+ Qb7 13. Qe8+ Ka7 14. Be3+
11. Qa4+ Kb7 12. Qb5+ Ka8 13. Bd6 and wins.
3. - Rb1+ 4. Rd1 Rxd1+ 5. Bxd1 (Kxd1?) Ra1 6. Ke2 drawn. But not 4. Bd1? Re5+ 5. Re2 Rxe2+ 6. Kxe2 Ra1 zugzwang.
4. Rd1? Rxd1 5. Bxd1 Rb1 6. Ke2 Ra1 zugzwang.
4. - Re4+ 5. Re2 Rxe2+ 6. Kxe2 and it's a draw. White to play would lose, but Black to play cannot maintain the bind.
Very neat. In two complementary variations we see the dual avoidance on move four in view of the upcoming position of mutual zugzwang on the sixth move.
Knowing the name of the composer may help you to find the theme of a study. Most of them, I guess, have certain preferences.
If there are not so many pieces involved, you may consult books on endgame theory like Fundamental Chess Endings by Karsten Müller and Frank Lamprecht. Or maybe it's a special type of endgame, e.g. with rooks. There are special monographs and if you're the proud owner of such a book you could find hints there.
In general, even if you don't have additional aids at hand, you simply have to play a series of moves and see what is the outcome. Sooner or later, you either have a total mess or you can say it's a draw/win. Check the line for blunders and choose better moves. Now, reiterate through your line and look for improvements and alternative lines. Ask yourself what threats do emerge, what are important squares, etc. You will definitely discover several hidden treasures of the study.
What to do when stuck?
If you think that there's no way for Black to defend properly, that White wins/draws with ease, then you surely have overlooked something. Maybe you missed exactly the defence that even spoils all your plans for White. For example, there could be a zwischenzug instead of an immediate recapture or direct reply to a threat.
On the other hand, it may appear that there is no appropriate continuation for White. Then you could experiment with sacrifices, change the order of the moves or examine checks. Consider what ways there are to draw — stalemate, perpetual check, insufficient material, etc. Likewise, how can White win — mate, pawn promotion, material advantage, and so on.
That's all, I'd say. Of course, in case you try to solve using a real chessboard, you should make sure that all pieces are set up correctly. Especially when examining (side)lines of your supposed solution, make sure to put back the pieces in the correct places after returning to the respective superordinate line. However, from time to time, diagrams are misprinted. And databases may contain wrong positions, too. Well, that's plain bad luck.