As you can see on the title, this is the summoning system. As for the ranks shown below please read the following.
D ranked- 1 creature
C ranked- 2 creatures
B ranked- 4 creatures
A ranked- 8 creatures
S ranked- 10 creatures
If you want to now how to make a summoning please click the bottem link
http://naruto.wikia.com/wiki/Summoning_Technique
As for puppets that leads us a different story. Puppets are summoned from scrolls or signs. Puppets can do many things and have to be controlled from chakra threads.
D ranked- 2 puppets
C ranked- 5 puppets
B ranked- 7 puppets
A ranked- 10 puppets
S ranked- 100 puppets
X-ranked- 105 puppets
http://naruto.wikia.com/wiki/Puppet.