In looking at how we practically use our spirit to the engage with the Holy Spirit there is a key verse in the Old Testament and a key passage in the New Testament.
27 The spirit of a man is the lamp of the Lord,
Searching all the inner depths of his heart. Proverbs 20:27 (NKJV)
The Lord engages with and uses our spirit. I think it is key to note that while those who walked with the Lord in the Old Testament were not born again as in the New Testament, they still had a functioning spirit, just one that did not possess Jesus nature and character. Hence the statement in Proverbs that the Lord uses our spirit to engage with us. We see this clearly in the examples already provided regarding Isaiah and Mary (Is. 26:9, Lk. 1:46-47). Now Paul further explicates this process for believers.
9 But as it is written:
“Eye has not seen, nor ear heard,
Nor have entered into the heart of man
The things which God has prepared for those who love Him.”
10 But God has revealed them to us through His Spirit. For the Spirit searches all things, yes, the deep things of God. 11 For what man knows the things of a man except the spirit of the man which is in him? Even so no one knows the things of God except the Spirit of God. 12 Now we have received, not the spirit of the world, but the Spirit who is from God, that we might know the things that have been freely given to us by God. 1 Corinthians 2:9–12 (NKJV)
Paul has two primary points in the broader passage. In the verses above he highlights that we know spiritual things by our spirit interacting with the Holy Spirit. Previously in 1 Corinthians 2 his point was that spiritual realities are not understood through natural wisdom (vs 1, 6) but through the wisdom of God (vs. 7).
So, given what the scriptures teach let us consider how this works in practice. I believe and experience that my mind and spirit both need to be involved. I generally get a sense of something deep inside. I experience something as Proverbs 20:27 says, in the ‘inner depths’ of my heart. A reference note in my bible says the Hebrew literally says, ‘rooms of the belly.’ That is in fact where I have a sense of Him speaking or drawing me to something. It may be a sense to do something, call someone or look up a verse or passage of scripture. I then need to engage my mind and exercise discernment regarding what I am sensing. I may also need to seek wisdom from others. The main point here is that the process is very practical. Spiritual things are not meant to be mysterious or esoteric, they are meant to aid us in our day to walk with Him from a surrendered and humble heart.