These are fascinating verses both for what they say and what they don't say. In general, what strikes me is that the author to the Hebrews cares more about mutual encouragement during the church gathering than he does about any specific activities that may take place.
When we think about the assembled body of Christ, we often fall into a bit of a trap. We tend, myself included, to think through various things that are going to happen: praying, singing, teaching, eating, testifying, giving a revelation, reading scripture, etc., etc. In these two above verses, the author doesn't speak about any of those things. I'm not suggesting that they aren't important, but the author of this letter appears to believe that the specific activities are less important than the overall building up of the body.
What does the author (whoever it was) focus upon? We see that he desires that the believers continue their practice of gathering together. He doesn't tell them when, where, or how often. Instead, his focus is on the why. He instructs the readers to consider one another. The focus of the Christians, therefore, in the gatherings should be others (not self).
Specifically, they are to think about how they can stir up or provoke each other. This must take place in the context of conversations. The author goes on to say that they should encourage one another. This clearly implies that as the church assembles there will be plenty of time and opportunity for the people to speak with each other. This requires both time and a setting that allows for this. Of course, this could occur just about any place or time, not exclusively when the entire church family comes together.
The author also tells the Hebrew Christians what they are to stir up. His hope is that they provoke each other to love and good works. He sees a connection between these two things. This corresponds to the rest of scripture which shows us that good works evidence true Christian love.
Taking it all together, the author to the Hebrews expects Christians to gather regularly in order to stir up, provoke, exhort, encourage, etc. each other to loving, good works. We can safely assume that this refers to works both in the church and in broader society. As they gather, his goal for them is mutual edification that leads to Christlike, sacrificial living.
I'm not suggesting that the author does not care at all about the specifics of what they do when they come together. For example, he would probably prefer scripture reading, eating, and prayer over puppets, wet willies, and MTV. However, that is not his focus here. He makes a point of focusing upon what seems to be most important in church gatherings: that the body assembles in order to stir itself up to love and good works.
You may ask, "Where is God in all this?" The answer is that He is right at the center of it. The reason? The church mutually edifies itself in Christ. Apart from Him, none of this happens. He is the source, the reason, and the outcome.
Peter speaks to this in I Peter 4:8-11, "Above all, keep loving one another earnestly, since love covers a multitude of sins. Show hospitality to one another without grumbling. As each has received a gift, use it to serve one another, as good stewards of God's varied grace: whoever speaks, as one who speaks oracles of God; whoever serves, as one who serves by the strength that God supplies - in order that in everything God may be glorified through Jesus Christ. To him belong glory and dominion forever and ever. Amen."
God receives the glory when we use our gifts to build up one another in Christ. This building up should lead to increased spiritual maturity that shows itself through loving, sacrificial service to the church and neighborhood.
As we gather, let's focus more on stirring up one another than on the specific activities of the assembling.