Whether you realize it or not, people meditate on things every day. Often we relive, rethink, and ponder things that upset us: the rude comment said to us, our worries about an upcoming performance, that car that cut us off in traffic, etc. But playing over events, possibilities, and considering outcomes in our mind more often than not leave us upset, fearful, or disturbed.

Some forms of meditation seek to empty the mind of thoughts or repeat a certain syllable to calm the mind. Christian mediation departs from those models in a very significant way. Christian mediation is filling the mind with thoughts of God, His actions, and His blessings for our lives. It is not seeking to avoid thoughts, rather it is creating and encouraging new thoughts.

The Bible contains many statements about meditation as practiced by Jews and Christians centuries ago:

this Book of the Law shall not depart from your mouth, but you shall meditate in it day and night, that you may observe to do according to all that is written in it. For then your will make your way prosperous, and then you will have good success. (Joshua 1:8, New King James Version)
You will keep him in perfect peace, whose mind is stage on You, because he trusts in You. (Isaiah 26:3, New King James Version)

Be anxious for nothing, but in everything by prayer and supplication, with thanksgiving, let your requests be made known to God; and the peace of God which surpasses all understanding, will guard your hearts and minds through Christ Jesus. (Philipians 4:6
, New King James Version) Hear my voice, O God, in my meditation; preserve my life from fear of the enemy. (Psalm 64:1, New King James Version)
Be angry, and do not sin. Meditate within your hear on your bed, and be still. (Psalm 4:4, New King James Version) My mouth shall speak wisdom, and the meditation of my heart shall give understanding. (Psalm 49:3, New King James Version)

Oh, How I love your law! It is my meditation all the day. You, through Your commandments, make me wiser than my enemies; for they are ever with me. I have more understanind gthan all my teachers, for your testimonies are my meditation. (Psalme 119:97-99, New King James Version)
I call to remembrance my song in the night: I meditate within my heart, and my spirit makes diligent search. (Psalm 77:6, New King James Version) Let the words of my mouth and the meditation of my heart be acceptable in Your sight, O LORD, my strength and my Redeemer. (Psalm 19:14, New King James Version)

May my meditation be sweet to Him; I will be glad in the LORD. (Psalm 104.34, New King James Version)
When I remember You on my bed. I meditate on You in th enight watches. (Psalm 63:6, New King James Version)

In order to meditate you need to place something in your mind to think about. You can memorize verses of the Bible and then think about them, pray through them, make songs out of them, and study them. You will be surprised at how this practice will greatly improve your life.

A good place to start is to memorize and meditate on the 1st Psalm:

BLESSED is the man
Who walks not in the counsel of the ungodly,
Nor stands in the path of sinners,
Nor sits in the seat of the scornful;

But his delight is in the law of the LORD,
And in His law he meditates day and night.

And he shall be like a tree planted by the rivers of water, that bringeth forth his fruit in his season;
his leaf also shall not wither; and whatsoever he doeth shall prosper.

The ungodly are not so,
But are like the chaff which the wind drives away.

Therefore the ungodly shall not stand in the judgment,
Nor sinners in the congregation of the righteous.
For the LORD knows the way of the righteous,
But the way of the ungodly shall perish.
(New King James Version)

Christian meditation considers beautiful things as well:

Finally, brethren, whatever things are true, whatever things are noble, whatever things are just, whatever things are pure, whaterver things are lovely, whatever things are of good report, if there is any virtue and if there is anythings praiseworthy--meditate on these things. (Philippians 4:8, New King James Version)