Different Kinds of Baptism
Baptism generally refers to some kind of immersion (normally water).
In fact, the Greek word for baptism is "baptizo" which means "to immerse".
There are different kinds of baptism.
Baptized With the Holy Spirit
I indeed baptize you with water unto repentance. but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with fire.
- Matthew 3:11 (KJV)
By far the most important baptism is that of the Holy Spirit.
When you become a new-born Christian you are automatically baptized with the Holy Spirit.
All you need to do is believe.
But this spake he of the Spirit, which they that believe on him should receive: for the Holy Ghost was not yet given; because that Jesus was not yet glorified.
- John 7:39 (KJV)
When we believe God places His Spirit in our heart.
A new heart also will I give you, and a new spirit will I put within you: and I will take away the stony heart out of your flesh, and I will give you an heart of flesh. And I will put my spirit within you, and cause you to walk in my statutes, and ye shall keep my judgments, and do them.
- Ezekiel 36:26-27 (KJV)
God's Law is written in our mind and heart.
For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people.
- Hebrews 8:10 (KJV)
Being baptized with the Holy Spirit is sometimes also referred to as being sealed.
In whom ye also trusted, after that ye heard the word of truth, the gospel of your salvation: in whom also after that ye believed, ye were sealed with that holy Spirit of promise. Which is the earnest of our inheritance until the redemption of the purchased possession, unto the praise of his glory.
- Ephesians 1:13-14 (KJV)
We are led by the Holy Spirit.
For as many as are led by the Spirit of God, they are the sons [children] of God.
- Roamns 8:14 (KJV)
It is the Holy Spirit that teaches us all things, and brings all things to our remembrance.
But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you.
- John 14:26 (KJV)
It is by the Holy Spirit that we are raised from the dead.
But if the Spirit of him that raised up Jesus from the dead dwell in you, he that raised up Christ from the dead shall also quicken your mortal bodies by his Spirit that dwelleth in you.
- Romans 8:11 (KJV)
Baptized with water
Sometimes people think you have to get baptized with water to receive the Holy Spirit, but that's not true (see above).
Being baptized with water is all about showing your commitment to God.
Jesus teaches us that we should all get baptized.
Jesus answered, Verily, verily, I say unto thee, Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God.
- John 3:5 (KJV)
Some people have suggested that if you're not baptized you are not saved, but I don't think Jesus would ever turn someone away who is a child of God, and has genuinely tried to get baptized. I suppose we can always baptize people just before they are about to enter the kingdom of God. That said however, baptism is important, and you should strive to do it if you can.
Jesus got baptized, and so should you.
And Jesus, when he was baptized, went up straightway out of the water: and, lo, the heavens were opened unto him, and he saw the Spirit of God descending like a dove, and lighting upon him: And lo a voice from heaven, saying, This is my beloved Son, in whom I am well pleased.
- Matthew 3:16-17 (KJV)
Most people get baptized in front of their family and friends, making baptism a unique opportunity to testify.
Baptism by water is an adult decision, and should be full immersion.
Baptized with fire
To understand what the baptism of fire is, we need to look at the context of the baptism verse at the top.
I indeed baptize you with water unto repentance. but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with fire: whose fan is in his hand, and he will throughly purge his floor, and gather his wheat into the garner; but he will burn up the chaff with unquenchable fire.
- Matthew 3:11-12 (KJV)
The phrase "wheat and chaff" is clearly a reference to judgment.
For our God is a consuming fire.
- Hebrews 12:29 (KJV)
And to the lake of fire.
He that overcometh shall inherit all things; and I will be his God, and he shall be my son. But the fearful, and unbelieving, and the abominable, and murderers, and whoremongers, and sorcerers, and idolaters, and all liars, shall have their part in the lake which burneth with fire and brimstone: which is the second death.
- Revelation 21:7-8 (KJV)
In day-to-day life a baptism of fire is sometimes also referred to as a "fiery trial".
Baptized with suffering
There is also the baptism of suffering. This mostly refers to Jesus, and to the cup that He had to drink.
But Jesus answered and said, Ye know not what ye ask. Are ye able to drink of the cup that I shall drink of, and to be baptized with the baptism [of suffering] that I am baptized with? They say unto him, We are able.
- Matthew 20:22 (KJV)
When someone "shines" in suffering (perseveres) he brings glory to God, as it shows the true Christian character of someone. Suffering is a kind of refining process.
When we share in the suffering, we will also share in the glory.
Beloved, think it not strange concerning the fiery trial which is to try you, as though some strange thing happened unto you: But rejoice, inasmuch as ye are partakers of Christ's sufferings; that, when his glory shall be revealed, ye may be glad also with exceeding joy.
- 1 Peter 4:12-19 (KJV)
It has been said that today's suffering is "nothing" compared to the glory we will receive.
For I reckon that the sufferings of this present time are not worthy to be compared with the glory which shall be revealed in us.
- Romans 8:18-31 (KJV)
When we suffer we grow especially close to God.
Doesn't make it any easier of course. 
Conclusion
So yeah, the baptism of the Holy Spirit you get by believing.
If you're not already baptized (in water), definitely look into that.