The expression 行ってきます is very common, especially in spoken Japanese.
While it literally means I will go and then come, which sounds awkward and a little redundant in English, it is totally acceptable in Japanese.
It is used mostly by family members, for example when leaving home in the morning to go to work or school.
The standard reply to 行ってきます is 行ってらっしゃい, which literally means Go and come back.
I'm leaving (the house).
Take care. Come back safely.
When returning home
When back home you say ただいま, to which the response is お帰りなさい.
お帰りなさい。 okaeri nasai.
Before eating you say 頂きます, and after eating you say ご馳走さまでした.