(Important note: These are suggestions rather than rules, with the exception of any biblical commands that are referenced.)
If you’re not ready to pursue marriage yet, because of parental rules or your own choice:
Relate to members of the opposite sex as brothers or sisters (1 Tim. 5:1-2), and guard your heart against other thoughts and feelings. Be open with your parents about all of your relationships, and ask them to fulfill their responsibility of providing counsel, protection, and accountability for you (Eph. 6:1-2, 1 Cor. 7:36-38). If your parents aren’t able or willing to do those things, seek that help from spiritual leaders (Heb. 13:17).
Stay in groups, don’t spend much time alone with any individual of the other sex (Prov. 4:23, Matt. 6:21). And be friends; if you do spend time together, do it as friends rather than as a “couple” or “boyfriend/girlfriend.”
If you do get too far along (“too close too soon”), mutually agree to separate totally for a while (principle of “radical amputation” from Matt. 5:29-30).
Commit yourself to serving Christ with the time and energy you have (1 Cor. 7:32-35), and find ways to fill your life with learning, work, and other ministry.
Stay away from media and other influences that will cause you to long for romance or will generate sexual desires (Rom. 13:14).
Use this time as a single young person to grow in Christ, and to learn and practice what the Bible says about good relationships, and to pray and prepare for the right kind of marriage based on biblical principles (Prov. 31, Eph. 5:22-33, 1 Timothy 3, Titus 2, etc.).
Evaluate carefully, and with godly counsel, the reasons why you or your parents think you are not ready to pursue marriage. Determine if they are really biblical, wise, and legitimate reasons, especially if you are good friends with someone who could be a good life partner for you (Prov. 31:10 11).
When you are ready to “date/court” for the purpose of marriage:
Pray a lot about this and prepare your heart and life to be a godly partner for someone, and evaluate any possible partners according to biblical principles and godly counsel from others—not according to feelings, physical attraction, pressure to get married, etc.
Until you meet someone that you want to “date/court,” or if a relationship doesn’t work out, learn and practice being content with the situation of “singleness” you are in (1 Cor. 7:17-24, Phil 4:11).
If a man wants to pursue a relationship beyond friendship with a woman, he should seek permission/approval from her father (or her spiritual leaders, if the father is not fulfilling his responsibility biblically). They should continue to be accountable to such protection and guidance, and should again seek permission/approval for engagement, if things go well (1 Cor. 7:36-38).
Fill the dating/courtship stage with worship, Bible Study, prayer, and ministry together, rather than merely the world’s ways of “dinner and a movie,” etc. Communicate openly about your intentions and plans, focus on serving the other person, and stay away from sexual sin, so that if it doesn’t work out it will not result in a debilitating “heartbreak” for either party.
When you get engaged, make it a short engagement, and get married even earlier if sexual sin is an issue (1 Cor. 7:8-9). But practice self-control and purity even in the engagement period, because if you don’t the problem will carry over into your marriage.
Get some good biblical premarital counseling (Preparing for Marriage God’s Way by Wayne Mack would be good homework), don’t go into debt on the wedding, and live happily ever after (for the glory of God)!
(For further study I suggest reading Josh Harris’s I Kissed Dating Goodbye and Doug Wilson’s Her Hand in Marriage: Biblical Courtship in the Modern World. Those books aren’t perfect, of course, but when read with discernment I think the issues they raise are important to consider.)