What does 2 Timothy 2:15 mean?

We do not have to make ourselves acceptable unto God. God delights in us and has given us every spiritual blessing possible because we are in Christ (Ephesians 1:3). Indeed, we are known and chosen by Him and are viewed as holy and blameless in His sight (Ephesians 1:4). You cannot get more approved than that. In Christ we have all that the Son has been given and, as Jesus Himself said,"The Father delights to give us the Kingdom. (Luke 12:32)" Give. Not make available to earn; but give. We who are Christ's are indeed God's children (Ephesians 1:5) and what God has laid up for us in heaven as an inheritance shall never change or pass away (1 Peter 1:4). But the passage you raise has nothing to do with our salvation (which is fixed and sure); instead, it focuses on what we might view as heavenly rewards; for the Bible is clear that there are varying degrees of reward in Heaven (Matthew 5:19,30; 6:19-21; Colossians 3:1-3; 1 Corinthians 3:11-15).

That given as context, let's look at your questions. The problem you are having perhaps stems in part from the fact that in places the NLT is overly dynamic as a translation. It thus wanders more into a paraphrase which, as with all paraphrases, is an interpretation of the meaning of a passage rather than a literal rendering of it. Paraphrases are intended to give the reader a better understanding (in the mind of the "translator") of what the original writer of the passage was saying. 2 Timothy 2:15 is a good case in point.

As is noted in your post, the verse reads:

Work hard so you can present yourself to God and receive his approval. Be a good worker, one who does not need to be ashamed and who correctly explains the word of truth.

That first sentence logically causes you to raise your three questions because it seems to present a specific thought (being a hard worker in order to gain God's approval) while being somewhat separate from the thought of the second sentence (being an accurate worker in handling God's Word). However, both sentences are actually a fleshing out of just one thought (apply your self zealously to God's work in the same way that any worker should zealously apply him or herself to a task in order to please their employer.) The Greek makes this clear.

Σπούδασον [be eager, be zealous] σεαυτὸν [yourself] δόκιμον [approved — by being found genuine as a result of practical proof] παραστῆσαι [to present, to show] τῷ Θεῷ [to God] ἐργάτην [a worker] ἀνεπαίσχυντον [not to be ashamed] ὀρθοτομοῦντα [cutting straight — ie: accurately handling] τὸν λόγον [the word] τῆς ἀληθείας [of truth]. Literally, then, the Greek is saying "Be zealous to present yourself as approved unto God, a worker not ashamed, accurately handling the Word of Truth (ie: the Scriptures)." So, placing that into an easily readable and understandable English form we can say it this way: "Be eager to show God you are genuine, a worker who needs not be ashamed, by dealing with His Word accurately."

In this way we see that your three questions (what does it mean to work hard? what does it mean to be a good worker? what does it mean not to be ashamed?) are answered by the text itself. To "work hard", as the NLT somewhat inaccurately puts it, is "to be dedicated to the task." To be a "good worker" is "to be "dedicated to the task of accurately presenting God's Word to others." The result of the foregoing is that we need never "be ashamed" before men (because we cannot share the full truth of God's Word with them) or "be ashamed" before God (because we fail to accurately convey God's all-important Word to them.)

BTW, while this is the apostle's instruction and exhortation to a young pastor, the fact that the Holy Spirit ensured it was included in the NT canon shows that it is a valid instruction for ALL who name the name of Christ in truth.

I pray this helps.