How to receive the gift of tongues according to the New Testament? 1 Corinthians 14:39 (NIV)
  
  Therefore, my brothers and sisters, be eager to prophesy, and do not
  forbid speaking in tongues.


In the early church, the gift of tongues was a common gift which almost everyone received, as we see in the church in Corinth as an example. Paul had to give advice on how to utilize their spiritual gifts in an orderly manner in the church.

However, I can't find any specific method/instruction given in the New Testament on how to receive the gift of tongues. If I want to receive the gift of tongues, what must I do? Is there any instruction given in the New Testament on how to receive the gift of tongues?
The New Testament does not give us a method for receiving the gift of tongues.  On the contrary, we are taught that the Holy Spirit distributes various gifts according to His own will.  Thus, it may not be His will that you or me receive the gift of tongues.

The twelfth chapter of 1 Corinthians is the key text on all of this:


  4 Now there are varieties of gifts, but the same Spirit. 5 And there are varieties of ministries, and the same Lord. 6 There are varieties of effects, but the same God who works all things in all persons. 7 But to each one is given the manifestation of the Spirit for the common good. 8 For to one is given the word of wisdom through the Spirit, and to another the word of knowledge according to the same Spirit; 9 to another faith by the same Spirit, and to another gifts of healing by the one Spirit, 10 and to another the effecting of miracles, and to another prophecy, and to another the distinguishing of spirits, to another various kinds of tongues, and to another the interpretation of tongues. 11 But one and the same Spirit works all these things, distributing to each one individually just as He wills.  1 Corinthians 12:4-11 NASB


So, the Spirit will give believers gifts as He Himself wills--not as we will.  We may desire the greater gifts, but that is all.  From the following passage, it appears the the gift of tongues is not considered one of the greater gifts, as apostleship, prophecy and teaching are given as the first three.


  27 Now you are Christ’s body, and individually members of it. 28 And God has appointed in the church, first apostles, second prophets, third teachers, then miracles, then gifts of healings, helps, administrations, various kinds of tongues. 29 All are not apostles, are they? All are not prophets, are they? All are not teachers, are they? All are not workers of miracles, are they? 30 All do not have gifts of healings, do they? All do not speak with tongues, do they? All do not interpret, do they? 31 But earnestly desire the greater gifts.  1 Corinthians 12:27-31