What are the most popular defences White should be prepared to fight against in the Ruy Lopez? Could you put the move orders as well as briefly explain the idea of the defenses?
The mainlines and key ideas are highlighted in wikipedia. The article covers:

Morphy Defence: 3...a6


Exchange Variation: 4.Bxc6
Norwegian Defence: 4.Ba4 b5 5.Bb3 Na5
Variations combining 3...a6 and ...Bc5
Steinitz Defence Deferred: 4.Ba4 d6
Schliemann Defence Deferred: 4.Ba4 f5
Arkhangelsk Defence: 4.Ba4 Nf6 5.0-0 b5 6.Bb3 Bb7
Mackenzie Variation 4. Ba4 Nf6 5.d4
Russian Defence: 4.Ba4 Nf6 5.0-0 d6
Open Defence: 4.Ba4 Nf6 5.0-0 Nxe4


Closed Defence 4.Ba4 Nf6 5.0-0 Be7


Delayed Exchange Variation Deferred: 6.Bxc6
Centre Attack: 6.d4
Worrall Attack: 6.Qe2
Averbakh Variation: 6.Re1 d6
Trajković Variation: 6.Re1 b5 7.Bb3 Bb7
Marshall Attack: 7...0-0 8.c3 d5


Main line: 4.Ba4 Nf6 5.0-0 Be7 6.Re1 b5 7.Bb3 d6 8.c3 0-0


Pilnik Variation: 9.d3
Yates Variation and Bogoljubow Variation: 9.d4
Chigorin Variation: 9.h3 Na5
Breyer Variation: 9.h3 Nb8
Zaitsev Variation: 9.h3 Bb7
Karpov Variation: 9.h3 Nd7
Kholmov Variation: 9.h3 Be6
Smyslov Variation: 9.h3 h6
Smyslov Variation: 9.h3 Qd7


Black defences other than 3...a6


Cozio Defence: 3...Nge7
Smyslov Defence: 3...g6
Bird's Defence: 3...Nd4
Steinitz Defence: 3...d6
Schliemann Defence: 3...f5
Classical Defence: 3...Bc5
Berlin Defence: 3...Nf6