Jude 1:20

But you, beloved, building yourselves up on your most holy faith; praying in the Holy Spirit.

With all prayer and petition pray at all times in the Spirit (“in the power of the Holy Spirit” – NLT; “by means of the Spirit” Wuest,) and with this in view, be on the alert with all perseverance and petition for all the saints, (Ephesians 6:18)

In a prophetic OT passage, which will be fulfilled in the believing remnant of Jews at the Second Coming of the Messiah, the prophet Zechariah writes…
And I will pour out on the house of David and on the inhabitants of Jerusalem, the Spirit of grace and of supplication (prayer), so that they will look on Me (Messiah) Whom they have pierced; and they will mourn for Him, as one mourns for an only son, and they will weep bitterly over Him, like the bitter weeping over a first-born. (Zechariah 12:10)

Paul also describes the role of the Holy Spirit and prayer in Romans 8 but this is not us praying in the Spirit but the Spirit Himself praying for us
In the same way the Spirit also helps our weakness; for we do not know how to pray as we should, but the Spirit Himself intercedes for us with groanings too deep for words. (Ro 8:26)

(Amplified Version) So too the [Holy] Spirit comes to our aid and bears us up in our weakness; for we do not know what prayer to offer nor how to offer it worthily as we ought, but the Spirit Himself goes to meet our supplication and pleads in our behalf with unspeakable yearnings and groanings too deep for utterance.

Although we could answer this in much greater detail below, how can a believer continually pray in the Spirit? Although it might seem paradoxical, the simple answer is that we can pray in the Spirit…
By continually depending on the Spirit!
By continually being filled with the Spirit!
By continually being controlled by the Spirit!