〜ていく

1. to do something and then go
2. to go (in a direction away from the speaker) by means of an action
3. to continue doing/changing/growing

いく

1. 毎朝、朝ごはんを食べて行きます。I eat breakfast and then go (to somewhere) every morning.
2. がっこうへあるいて行きます。I walk to school. (I go to school by walking.)
3. 日本語を毎日れんしゅうしていきます。I will continue practicing Japanese every day.
3. だんだんあたたかくなっていきます。It will gradually get warmer.

〜てくる

1. to do something and then come
2. to come (in a direction toward the speaker) by means of an action
3. begin to, come to, is in progress

くる

1. 朝ごはんを食べて来ました。I ate breakfast and then came here.
2. 毎日がっこうへあるいて来ます。I walk to school everyday. (I come to school by walking.)
3. 日本語がわかってきました。l have started understanding Japanese.
3. だんだんあたたかくなってきました。It is gradually getting warmer.