Pentecost Novena

The Pentecost Novena is the first of all novenas, nine days of prayer. After Jesus' Ascension into heaven, He commanded His disciples to come together in the upper room to devote themselves to constant prayer (Acts 1:14). They prayed for nine days before receiving the Holy Spirit on Pentecost.
-Presentation Ministries: Pentecost Novena

Jesus instructed the apostles to go to Jerusalem and wait for the Holy Spirit. This was actually the first novena in preparation of Pentecost - Novena to the Holy Spirit.
-About: Ascension of the Lord

About: Roman Catholicism Novena to the Holy Spirit

Novena: Ascension Through Pentecost
Prayer guides for the nine days leading up to Pentecost.

Fr. Pat's Place: Pentecost Novena

The Burning Bush Pentecost Novena

Novena: A nine days' private or public devotion in the Catholic Church to obtain special graces.
-Catholic Encyclopedia: Novena

That's what the disciples had to do - just sit still and wait. "Don't leave the city until..." Why did Jesus make them wait? I think it was as much the sitting still as the waiting that was the point of the exercise. Just waiting a while, if you were getting on with other stuff in the meantime, wouldn't be any big deal really. But having to SIT STILL - not travel about, not distract yourself with other things, just reach a place of stillness - meant that when the Spirit came they were ready to handle it. They weren't just waiting, passively, FOR something to happen. It was an active, expectant waiting - like the phrase from the Psalms, they were 'Waiting ON God'.
-maggi dawn

Then, placing their trust in the word of Jesus, which would henceforth be their only support, they returned to Jerusalem where, in the Cenacle, they awaited in prayer the fulfillment of the promise. It was the first novena in preparation for Pentecost: "All these were persevering with one mind in prayer with... Mary, the Mother of Jesus" (Acts 1:14).

Silence, recollection, prayer, peace with our brethren, and union with Mary: these are the characteristics of the novena we too should make in preparation for the coming of the Holy Spirit.
-Catholic Culture: Liturgical Year: Solemnity of the Ascension, excerpted from Divine Intimacy, Fr. Gabriel of St. Mary Magdalen, O.C.D.