I'm not sure what the 2Timothy passage has to do with it, but the 1 Corinthians passage makes it very plain that in our mind we have no clue of the Spirit of God or even our own spirit. The problem arises when (most) people identify with their mind. When they say this is me, they say it from the same carnal mind that is unable to discern these things.
What do you tell those people when they ask, how do I worship in spirit?
We are in the last days so I think it is safe to say that, the hour has come which Jesus spoke about. As Believers, we should now be praying and worshipping in spirit. So now you have a big group of Believers who love the Lord but unwittingly approach Him from the carnal mind, then pray to Him. Because they still identify with the flesh/their mind.
So how would one explain to these, how to do this?
2Ti 3:5 Having a form of godliness, but denying the power thereof: from such turn away.
Many have an outward appearance that seems to be holy to others as they come with their Sunday best and Bible in hand in appearance to sit for an hour, but yet have not the indwelling of the Holy Spirit nor the power of God as they have no relationship or fellowship with Him.
To worship in Spirit and truth means to have the indwelling of the Holy Spirit that teaches us all truths as one has that personal relationship with Christ Jesus.
Act 19:1 And it came to pass, that, while Apollos was at Corinth, Paul having passed through the upper coasts came to Ephesus: and finding certain disciples,
Act 19:2 He said unto them, Have ye received the Holy Ghost since ye believed? And they said unto him, We have not so much as heard whether there be any Holy Ghost.
Act 19:3 And he said unto them, Unto what then were ye baptized? And they said, Unto John's baptism.
Act 19:4 Then said Paul, John verily baptized with the baptism of repentance, saying unto the people, that they should believe on him which should come after him, that is, on Christ Jesus.
Act 19:5 When they heard this, they were baptized in the name of the Lord Jesus.
Mat 3:11 I indeed baptize you with water unto repentance: but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and with fire: (fire means empowerment)