I was told in order to go to heaven one must be saved, baptized, and blessed with the Holy Ghost. He also told me that you know you have the Holy Ghost when you start speaking in tongues out of nowhere. Is this true?
The Bible is all about being saved. One can not go to heaven unless he is saved from sin. That salvation comes when God forgives us of our sins. That forgiveness only comes after one is immersed in water, is baptized. Paul said that he was told, "arise, and be baptized, and wash away thy sins, calling on the name of the Lord." (Acts 22:16) Baptism is the point at which our sins are washed away. Sins after that time are covered by the blood of Christ beginning when we are baptized and continually cleansing us (1 John 1:7). So to go to heaven we must be saved, and that salvation comes when we are baptized. At the same time we are given the gift of the Holy Spirit (Acts 2:38). That spirit dwells in us (1 Corinthians 3:16; 1 John 4:13). That spirit is the promise that God will save us (Ephesians 1:13-14). So I think the Bible teaches that all three things you mention-being saved, being baptized, and being blessed with the Holy Spirit-all happen at the same time, although salvation and the indwelling of the Spirit may be said to continue from that time.
Does not being able to speak in tongues mean we don't have the Spirit? Does speaking in tongues mean we do? In both cases I think the answer is "no." Just because a person doesn't speak in tongues doesn't mean he doesn't have the Holy Spirit. Paul's discourse on the "gifts of the Spirit" (not to be confused with the "gift of the Spirit" in Acts 2:38) in 1 Corinthians, chapters 12 through 14, is probably the best passage on the various gifts that men may have received through the Holy Spirit. In the first part of chapter 12 he makes it clear that not everyone was given the gift of speaking in human languages they had not studied. (That is the biblical definition of "tongues," by the way.) In fact, in chapter 14 he points out that speaking in tongues was the least important of the gifts. If one's spirituality was based on which gift, if any, he had, then those who spoke in tongues would have been considered only marginally more spiritual than those who had no gift. Of course, the gifts were not based on how spiritual one was, but it is interesting that nowadays people tend to emphasize the least important gift. In any case, not everyone who had the Spirit spoke in tongues. On the other hand, not everyone who claims to have the gift of speaking in tongues has the Holy Spirit. The phenomenon, technically known as glossolalia, has been noted in many religions, including some that actively oppose Christianity. There are also many who claim the ability who can clearly be proven to be frauds, and therefore must not have the Spirit.
In the Bible, speaking in tongues specifically meant the ability to speak in a human language that the speaker had not learned through normal study. It was important in the first century because many of those who would be spreading the gospel would not know more than their home language. That it was human languages is obvious from Acts 2:6-11. Many who now claim the ability say they are speaking in some "heavenly" or "angelic" language. The problem is they aren't teaching the angels and aren't in heaven. Paul specified that if anyone was to speak in tongues there must be present somebody who could interpret (1 Corinthians 14:5, 13). So the first question to ask anyone who claims the ability is what language they are speaking in. If it is not a known, human language, then it is not scriptural speaking in tongues. (The King James Version of the Bible added to the confusion by inserting the word "unknown" when they translated the Greek word that is "tongues" or "languages.") The second thing to ask is what the person said. If he can not translate, then he is clearly not speaking as a result of the Spirit of God because that Spirit says he must have a translator.
Finally, there are many of us who say the Bible teaches that the ability to speak in tongues through the agency of the Holy Spirit ended almost 1900 years ago. Paul said in 1 Corinthians 13:8-10, "whether there be prophecies, they shall fail; whether there be tongues, they shall cease; whether there be knowledge, it shall vanish away. For we know in part, and we prophesy in part. But when that which is perfect is come, then that which is in part shall be done away." So tongues were to cease. When? He said it was when "that which is complete [perfect]" had come. Some say this is the second coming of Christ, or the judgement, but those are impossible because of the Greek grammar. Additionally, it can't be some time at or after the second coming of Christ, because at that time faith will end in sight, but Paul says that faith will outlast tongues. Many of us hold that "that which is complete" was the completion of the New Testament. After the scriptures were completed the gift of tongues became unnecessary.
Besides that, the ability to speak in tongues could only be received one way. It could only come by the laying on of an apostle's hands. Those who had the gift could not pass it on; only the apostles (and presumably Cornelius and his family) could do so. We learn this in Acts 8:14-19. Philip, who had the power to perform miracles, did not have the ability to impart such gifts. It was that ability which Simon tried to buy from the apostles. If only the apostles could impart the ability to perform miracles, such as speaking in tongues, then the ability to speak in tongues would have died with the last man on whom one of the apostles had laid his hands. Unless we have some 2,000-year-old apostles running around the ability to speak in tongues ended no later than around 150 or 175 AD, if not before then. So if someone claims the ability to speak in tongues because of the Holy Spirit, we should ask which apostle gave him that ability, and where this 2,000 year old man can be found so we can get the power, too.
The Holy Spirit is the word of God. We can have that Spirit dwelling in us, through our baptism and study of the Bible. We don't need to speak in tongues to prove that we have that Spirit. You know you have the Holy Spirit when your sins are forgiven at the point of immersion. In fact, to require speaking in tongues is evidence that one does not have much faith that the Spirit dwells within them.