As with many gifts of the Spirit, the gift of 'leadership' is not described in the Bible directly. The first conclusion I draw from that is the unique operations of The Holy Spirit do not require a user guide.
For example, at Pentecost the Bible says,
All of them were filled with the Holy Spirit and began to speak in other tongues as the Spirit enabled them.
There is no mention of 'preparation' for this unusual miraculous gift of speaking in foreign languages without any training. Peter did not say something like, 'Brothers the Spirit is about to come, when he does you will feel a burning and an urge to waggle your tongue. Do not be shy, give in to the waggle.' No the gifts do not need a user guide. The Spirit was powerful enough to produce the effect without any preparation.
There is a general guide for all gifts in the Bible, such as 'love' 'building up the body', etc. (1 Cor 12) Also these gifts (whichever of them are in operation today) are part of the 'ministry of the Spirit'. That is they are not just natural gifts sanctified by the Spirit, but are things given by the Spirit. They might not be in operation if we are living in sin. Just as Samson was not strong when his hair was cut, a natural born leader cannot lead without faith strengthened by the Spirit.
With regard to 'leadership' specifically, notice the scripture describes the gifts more by recording those who had them, than by doctrine. For example, we need not doubt that Paul had a gift of teaching.
Some in the Bible that were obvious spiritual leaders are: Joseph, David, Joshua, Jesus, Peter, Paul, Barnabas. Every church also has leaders, these are those people who others 'follow'. After the scripture we see great leaders in Church history as well, someone like Luther for instance.
As a final description let me just propose something. A leader is someone aware of the Spirit and burdened with God's love to lead people. They have an ability from the Holy Spirit to influence others towards Christ. People respect them and follow them, without necessarily realizing it. Leaders, who lead in the Spirit help the ministry of a local church strengthen. They see how others feel and express burdens of their brothers and sisters is a way that helps the church avoid sin. People follow their cue, even without words spoken. These are just random observations, but I think you can see what I mean, as manifest in the leaders I listed.
Having said this let me add, many leaders are in the making, and many leaders are only recognized by a few. Nobody recognized Noah's lead.
For an expert analysis on the gifts of the Holy Spirit I recommend, John Owen's Works Volume 4, his second volume on the subject.