In a standard Helpmate, stipulated as 'h#n' or 'h#n½' below the diagram, White and Black cooperate (ie 'help' each other) to checkmate Black.  Usually Black moves first, so a h#2 would require the sequence: black moves, white moves, black moves, white mates.  Thus, both sides typically make the same number of moves (for example: h#2, h#3, etc.).

However, a '½' in the stipulation (eg. h#3½) indicates that White moves first.  Whenever you see a '*', set/play exists; eg. 'h#2*' solves as a h#1½ and as a h#2.  The label 'h#2 duplex' means the problem solves as a normal h#2 (black starts, white mates), and then solves with roles reversed (white starts, black mates).  You'll often find twinning used (eg. 'c)Kg7→a5', 'd)Bc5↔Sd5', 'b) rotate 90', etc.) for helpmates with multiple parts; just make the change indicated to form another problem! 

8/5SR1/6PB/1P2P1P1/4P3/2p2p1p/pprp1p1p/kbqrbK2

Solution:  Click & hold left mouse button and highlight the area below:
 

1.h1S! Sd6 2.h2 Sf5 3.Sg3+ Sxg3 4.h1S! Se2 5.fxe2+ Kg2 6.f1S! Rc7 7.Bg3 Rxc3 8.Bxe5 Rxc2 9.Bg7 Rxc1 10.bxc1S! Bxg7#

8/3pb3/B2k4/8/4b2p/2P1Sp2/r1q2R1K/4r3

Solution:  Click & hold left mouse button and highlight the area below:

1.Ke6 Sg2! 2.fxg2! Rf5 3.d6 Bc8#
1.Ke5 Be2! 2.fxe2! Rf6 3.d5 Sg4# 

"A wonderful work with an accumulation of strategic elements, depicted with perfect technique." (Judge: János Csák)

Solution:  Click & hold left mouse button and highlight the area below:

1.Kf2 e4!(K~?) 2.Ke1 Sc6(Sc2?) 3.Rxe4+ Sb4 4.Re2 Sd3#
1.Sf2 g4!(K~?) 2.Sh1 Se6(Se2?) 3.Rxg4+ Sf4 4.Rg2 Sh3#