"Put to death, therefore, whatever belongs to your earthly nature: sexual immorality, impurity, lust, evil desires and greed, which is idolatry" (Colossians 3:5).
Commentaries I have read describe the earthly nature. But not much on how to put it to death.
To my reading it appears that Paul answers your question himself right in Colossians 3-4:
3:1 ... seek those things which are above ... 2 Set your affection on things above, not on things on the earth.
3:9 Lie not one to another ... 12 Put on ... bowels of mercies, kindness, humbleness of mind, meekness, longsuffering; 13 Forbearing one another, and forgiving one another, if any man have a quarrel against any: even as Christ forgave you, so also do ye. 14 And above all these things put on charity, which is the bond of perfectness.
3:15 ... let the peace of God rule in your hearts ... and be ye thankful. 16 Let the word of Christ dwell in you richly in all wisdom; teaching and admonishing one another in psalms and hymns and spiritual songs, singing with grace in your hearts to the Lord. 17 And whatsoever ye do in word or deed, do all in the name of the Lord Jesus, giving thanks to God and the Father by him.
3:18 Wives, submit yourselves unto your own husbands, as it is fit in the Lord. 19 Husbands, love your wives, and be not bitter against them. 20 Children, obey your parents in all things ... 21 Fathers, provoke not your children to anger ...
3:22 Servants, obey in all things your masters according to the flesh; not with eyeservice, as menpleasers; but in singleness of heart, fearing God: 23 And whatsoever ye do, do it heartily, as to the Lord, and not unto men;
4:1 Masters, give unto your servants that which is just and equal ... 2 Continue in prayer, and watch in the same with thanksgiving ...
4:5 Walk in wisdom toward them that are without, redeeming the time. 6 Let your speech be alway with grace, seasoned with salt, that ye may know how ye ought to answer every man.
There's a lot in there that's specific, to help us understand the words that aren't as clear.