Is there any method/instruction given by prominent preachers recently on how to receive the gift of tongues? Some specific way of prayer, some specific steps to follow, what kind of attitude is required and so forth?
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You are overlooking the most important word in your question, and that is 'gift'. A gift is something that is freely given - the giver chooses whether or not to give, and the receiver can only choose whether or not to accept it - if it is given. If the receiver can compel the giver in any way, or tries to earn it, then it isn't a gift. It's long been part of Christian theology that Tongues and rather supernatural abilities are 'gifts' in that sense. Check out 1 Corinthians 12, where this is made explicit. Also check out 1 Corinthians 13, which is an explanation of something better and more important than spiritual gifts - Love. It's not accidental that those chapters are next to each other.
General advice as far as I know is that if you earnestly desire a specific gift, keep praying for it. But be aware, as with all other prayers, God may not grant you what you are asking. He may have a better, alternative plan for you.
The exceptions to this are the Pentecostal traditions where speaking in tongues is a sure and necessary sign of being a true believer. In that case if you don't have that gift, consult with a Pastor.