You are correct, we are all given spiritual gifts (1 Corinthians 7:7; 1 Corinthians 12:7). And its great that you desire to discover and develop them. Paul counsels us to do exactly that (1 Corinthians 12:31, 1 Corinthians 14:1).
Lets take a look at the purpose of spiritual gifts:
1 Corinthians 14:12 (KJV)
12 Even so ye, forasmuch as ye are zealous of spiritual gifts, seek that ye may excel to the edifying of the church.
The purpose of spiritual gifts is to edify others. We cannot seek them for selfish purposes. This is why Paul jumps into a discourse about charity (the entire 13th chapter) in the middle of his discourse about spiritual gifts.
1 Corinthians 13:1-2 (KJV)
1 Though I speak with the tongues of men and of angels, and have not charity, I am become as sounding brass, or a tinkling cymbal.
2 And though I have the gift of prophecy, and understand all mysteries, and all knowledge; and though I have all faith, so that I could remove mountains, and have not charity, I am nothing.
So the first step is to make sure you're trying to develop your gifts for the right reason.
The next step is to pray. Ask God about what gifts you have, about which ones you should pursue, and about how to develop them. I know from personal experience that prayer makes a big difference.
From there its hard to give a step-by-step plan. It really depends on what gifts you have. Some of them are easily developed proactively while others are more circumstantial. For example, if its the gift of knowledge and/or wisdom, then you can study the Bible (and perhaps other edifying books). If its the gift of the interpretation of tongues, then you have to hear someone speak in tongues which is largely out of your control. However something you can do about the more circumstantial gifts is to pray for opportunities to practice them.