"친구가 개에게 영어를 가르칩니다."
Translation:The friend teaches English to the dog.
I looked it up and it also means “to”, so perhaps you need both characters here, but I don’t know why they each can be used individually or together and when each would be used.
I got the Korean English dictionary from Dict Box here, because it also offers English Korean and can be used offline.
Okay, I finally found something about indirect objects which explains more about this form: http://morninglands.com/indirect-object-particle-%ec%97%90%ea%b2%8c-%ed%95%9c%ed%85%8c-%ec%97%90/
So, it turns out that both characters are used for live animals or people as indirect objects which are recipients. So, if you give water to a plant, then you would only need the first character.
I don't think saying "my friend" would work in this sentence since it has no indication that it is your friend or someone else's.
The "-가" attached at the end of "친구" indicates that it is pointing out a specific friend that is your area, but doesn't tell you who's friend it is. I'm pretty sure if it were to say "my friend" the sentence would have "나의" somewhere in the mix.
Hope this helped (: and if I am wrong feel free to correct me!