The way to say 'I'm going to bed' in Spanish is the following: "Me voy a la cama'
To say "I'm going to sleep' then it is: 'Me voy a dormir'.
The meaning of the words is the following:
Me; Meaning 'I'
voy: (verb) going, go
a: to
la: (feminine form of the article) the
bed: (adjective): cama
dormir: (verb) sleep

Buenas Noches! (Good Night!)