Here's a few things I picked up about Paul's mentoring relationship with Timothy:

1:3 He urged him - particularly to protect correct teaching.
1:18 He instructed him - in how to live a life of faith.
2:1 He urged him to pray - to include God in everything he did.
3:1 He offers trustworthy sayings - some advice from an experienced Christian.
4:6 He presents him with ideas - about the future and Tim's decisions.
4:12 He encourages him - to not be ashamed of his age.
5:1 He issues warnings - on how to avoid bad situations.
5:21 He charges him - I think this is basically a postive way to describe giving him an order. At the very least it's a challenge.
6:11 He sounds the alarm - flee from sin!

1 Timothy 1:3, 1 Timothy 1:18, 1 Timothy 2:1, 1 Timothy 3:1, 1 Timothy 4:6, 1 Timothy 4:9, 1 Timothy 4:12, 1 Timothy 5:1, 1 Timothy 5:3, 1 Timothy 5:21 and 1 Timothy 6:11