Let me try to make it a little clearer for you!
"Which of you fathers, if your son asks for a fish, will give him a snake instead? Or if he asks for an egg, will give him a scorpion? If you then, though you are evil, know how to give good gifts to your children, how much more will your Father in heaven give the Holy Spirit to those who ask him!" (Luke 11:11-13)
The key to understanding this passage is that Jesus gives examples of a son asking his father for a gift, and then He says that "your Father" will give the Holy Spirit to those who ask. In other words, if you are a Christian, a child of God, then you can ask your Father for the Holy Spirit. First you must be saved (at which point God becomes your heavenly Father - see John 1:12-13, Galatians 3:26, and 4:4-7), then you can ask for the Holy Spirit. But remember, when we become saved we automatically receive the indwelling Holy Spirit, we don't have to ask for Him! Yet Jesus says that God will give the gift of the Holy Spirit to those who ask for it. This gift, therefore, is not salvation (because we do not become saved by asking God for the Holy Spirit), but instead this gift is what the Bible calls the "baptism" of the Holy Spirit for receiving spiritual empowerment:
"On one occasion, while he was eating with them, he gave them this command: "Do not leave Jerusalem, but wait for the gift my Father promised, which you have heard me speak about. For John baptized with water, but in a few days you will be baptized with the Holy Spirit. ... you will receive power when the Holy Spirit comes on you; and you will be my witnesses in Jerusalem, and in all Judea and Samaria, and to the ends of the earth."" (Acts 1:4-8)
"While Peter was still speaking these words, the Holy Spirit came on all who heard the message. The circumcised believers who had come with Peter were astonished that the gift of the Holy Spirit had been poured out even on the Gentiles. For they heard them speaking in tongues and praising God. Then Peter said, "Can anyone keep these people from being baptized with water? They have received the Holy Spirit just as we have."" (Acts 10:44-47)
"As I began to speak, the Holy Spirit came on them as he had come on us at the beginning. Then I remembered what the Lord had said: 'John baptized with water, but you will be baptized with the Holy Spirit.' So if God gave them the same gift as he gave us, who believed in the Lord Jesus Christ, who was I to think that I could oppose God?" (Acts 11:15-17)
This "baptism" is a gift of the Holy Spirit for receiving spiritual empowerment, and we can ask for this gift after we receive salvation (although God might sometimes give this gift to a person immediately after receiving salvation, as in Acts 10:44-47 and 11:15-17).
We can demonstrate this further by comparing Luke 11:13 with its parallel passage in Matthew:
"If you then, though you are evil, know how to give good gifts to your children, how much more will your Father in heaven give the Holy Spirit to those who ask him!" (Luke 11:13)
"If you, then, though you are evil, know how to give good gifts to your children, how much more will your Father in heaven give good gifts to those who ask him!" (Matthew 7:11)
Comparing these two passages, we can see that receiving the Holy Spirit is equated with receiving "good gifts." In other words, when we as Christians ask our Father for the Holy Spirit, He will give us the gift of being baptized with the Holy Spirit for our spiritual empowerment. Notice that salvation is not mentioned at all here, and in fact we do not become saved by asking for the Holy Spirit.
Since only Christians have been adopted as children of God (Ephesians 1:4-5), only Christians can ask our heavenly Father for the gift of the baptism of the Holy Spirit. This demonstrates that the baptism of the Holy Spirit is only available to us after salvation.