How can a young man seek holiness?
In order to answer your question, we need to explore that is meant by "holy."
The word “holy” translates a Hebrew word referring to something or someone dedicated to the service of a god. "Holy" includes dedication when it is applied to people and things, but it involves more than mere dedication. Holiness also means holding something or someone as extra special. God said He selected the people of Israel to be a holy nation (Deuteronomy 7:6). Concerning Israel, Moses said God “will set you high above all nations which He has made, in praise, in name, and in honor, and that you may be a holy people to the LORD your God, just as He has spoken” (Deuteronomy 26:19). But God also values righteousness as a part of holiness. “The LORD will establish you as a holy people to Himself, just as He has sworn to you, if you keep the commandments of the LORD your God and walk in His ways” (Deuteronomy 28:9). God told Israel that righteous action on their part would cause them to become a holy people. Their obedience to God would make them distinct and special among all the nations of the world.
The Israelites were told to, “distinguish between holy and unholy, and between unclean and clean” (Leviticus 10:10). The word translated here as “unholy” is the Hebrew word for “profane.” “Profane” means to pollute or treat something as common and of no value. When people throw trash down in a park, they are polluting it – they act as if the park as having no more value than a garbage dump.
"Therefore gird up the loins of your mind, be sober, and rest your hope fully upon the grace that is to be brought to you at the revelation of Jesus Christ; as obedient children, not conforming yourselves to the former lusts, as in your ignorance; but as He who called you is holy, you also be holy in all your conduct, because it is written, "Be holy, for I am holy." And if you call on the Father, who without partiality judges according to each one's work, conduct yourselves throughout the time of your stay here in fear; knowing that you were not redeemed with corruptible things, like silver or gold, from your aimless conduct received by tradition from your fathers, but with the precious blood of Christ, as of a lamb without blemish and without spot. He indeed was foreordained before the foundation of the world, but was manifest in these last times for you who through Him believe in God, who raised Him from the dead and gave Him glory, so that your faith and hope are in God. Since you have purified your souls in obeying the truth through the Spirit in sincere love of the brethren, love one another fervently with a pure heart, having been born again, not of corruptible seed but incorruptible, through the word of God which lives and abides forever" (1 Peter 1:13-23).
Peter's argument is that Christians are special people because they were bought at a special price -- by the very blood of the Son of God. Therefore, Christians should act as special people -- not by having their noses in the air, acting like they are better than everyone else -- but by purifying their lives through obedience to God's teachings. It is God's teachings that brought us into a special relationship with God and His Son, and it is those same teachings that make us different from the rest of the world and, thus, special.
You can't be holy by sinning. Sins are common and degrading. "I beseech you therefore, brethren, by the mercies of God, that you present your bodies a living sacrifice, holy, acceptable to God, which is your reasonable service. And do not be conformed to this world, but be transformed by the renewing of your mind, that you may prove what is that good and acceptable and perfect will of God" (Romans 12:1-2). You become holy by seeking to be righteous.