I'll share my thoughts. Essentially the same as Bro. Blume's. I just word it a little different.
Praying in the Spirit is praying as the Spirit leads you to pray, be it in tongues or your native language.
To be "in the Spirit" means to be in present and conscious awareness of the abiding presence of the Spirit within you. Having the Spirit we realize that Christ is in the Father, the Father in Christ, and Christ in us... through the Spirit. This abiding in us is more than merely the Spirit dwelling within us, it is the Spirit's presence and permeation of our spiritual being, our inner man. Through this abiding reality we become one spirit with the Lord (
I Corinthians 6:17) and branches of the vine, Jesus Christ (
John 15:5). These realities being so, we realize that we are living extensions of Christ Himself. Being in present conscious awareness of this spiritual reality is being "in the Spirit".
And "walking in the Spirit" is allowing the abiding presence of the Spirit to lead and guide you in your thoughts, actions, and decisions. It is the opposite of living in accordance to the law, as Bro. Blume stated. It is the daily, moment by moment, willingness to follow the Spirit's will and leading in all things as opposed to any codified list of laws, standards, or regulations.