2 Timothy 1:15-2:7

You are aware that all who are in Asia turned away from me, among whom are Phygelus and Hermogenes.  May the Lord grant mercy to the household of Onesiphorus, for he often refreshed me and was not ashamed of my chains,  but when he arrived in Rome he searched for me earnestly and found me— may the Lord grant him to find mercy from the Lord on that day!—and you well know all the service he rendered at Ephesus.
You then, my child, be strengthened by the grace that is in Christ Jesus, and what you have heard from me in the presence of many witnesses entrust to faithful men, who will be able to teach others also. Share in suffering as a good soldier of Christ Jesus. No soldier gets entangled in civilian pursuits, since his aim is to please the one who enlisted him. An athlete is not crowned unless he competes according to the rules. It is the hard-working farmer who ought to have the first share of the crops. Think over what I say, for the Lord will give you understanding in everything.

2 Timothy 1:15-2:7

Apparently, "all who are in Asia turned away from me" says Paul.  This is something that Timothy is already aware of.  He points out two people who have turned away from him, Phygelus and Hermogenes.  This next group perhaps is included among the people who have turned away from Paul, but I'm not entirely sure.  Paul actually speaks well of the household of Onesiphorus.  He often refreshed Paul and was not ashamed of his chains.  I guess being associated with someone in prison was not necessarily a good thing.  In fact, that's probably true nowadays.  Associating with prisoners may result in some kind of shame brought.  However, this is not true for the household of Onesiphorus.  Paul was strengthened and encouraged by the household of Onesiphorus.

On that same note, Paul turns to Timothy and encourages him to be strengthened.  Paul was helped by the household of Onesiphorus, but he now encourages Timothy to "be strengthened by the grace that is in Christ Jesus".  The next thing Paul tells Timothy is to pass along the message.  Paul preaches Christ and so teaches Timothy to preach as well.  Paul's death may come soon and he wants Timothy to do as he did and pass along the message to more people to carry it along.  It doesn't just end with Paul and it doesn't just end with Timothy.

Paul now presents Timothy with three pictures.  The first is of a good soldier of Jesus.  With this picture, Paul explains that a soldier doesn't bother himself with civilian matters.  Instead, a soldier's main goal is to please his officer.  The second picture is of an athlete.  An athlete can only properly win by following all the rules.  The last picture is of a hard-working farmer.  It is expected or perhaps due to the farmer that he enjoy the first share of his harvest.  After these three pictures, Paul simply tells Timothy to "Think over what I say".  I don't really know what they all mean.  Fortunately, Paul's instruction is to think it over.  God will give understanding, so I will ponder and think it over.