Believing is a Verb

There will always be a variety of action that will be taken pertinent to each situation, the important part is - God is the one with the power and ability. Believing is the action that unleashes the power.

Hebrews 11:1 Now faith is the substance of things hoped for,
    the evidence of things not seen.
:2 For by it the elders obtained a good report.

Faith is pistis in Greek; more appropriately translated believing. Don't get wrapped up in the action - sacrifice was used in the Old Testament to pay for sins because they didn't have the redeemer yet. Believing God is the heart of the matter. Believing is the action we take.

:3 Through faith we understand that the worlds were framed by the word of God,
    so that things which are seen were not made of things which do appear.
:4 By faith Abel offered unto God a more excellent sacrifice than Cain,
    by which he obtained witness that he was righteous,
    God testifying of his gifts:
    and by it he being dead yet speaketh.

    Abel believed God's Word when he offered the sacrifice to God, he believed what God said about sacrifices and Cain didn't. Cain put God's Word below him, he despised God's wisdom.

Proverbs 1:7  The fear of the Lord is the beginning of knowledge:
but fools despise wisdom and instruction.

 God looks on the heart. If his heart would have been right with God Cain's offering would be right on.

:5 By faith Enoch was translated that he should not see death; 
    and was not found, because God had translated him:
    for before his translation he had this testimony,
    that he pleased God.
:6 But without faith it is impossible to please him:
    for he that cometh to God must believe that he is,
    and that he is a rewarder of them that diligently seek him.

It is faith - not works that gets the results. We must believe and then God is the rewarder.

Hebrews 11:7 By faith Noah, being warned of God of things not seen as yet,
    moved with fear,
    prepared an ark to the saving of his house;
    by the which he condemned the world,
    and became heir of the righteousness which is by faith.
:8 By faith Abraham,
    when he was called to go out into a place
    which he should after receive for an inheritance,
    obeyed; and he went out, not knowing whither he went.

Abraham had a large household, there was one point that when he was out fighting with the king of Sodom that he had over 200 trained warriors in his household. In that culture many of those warriors had a wife and a couple of kids. This adds up to be 600, 800 or maybe even 1000 people, plus thousands of sheep, thousands of goats. In our culture Abraham's family was by our standards at this time a small town - now there is details that need to be worked out, you just don't pick up several hundred people tell them to jump in the busses and get on the road without a destination, yet this is what Abraham did. He believed God, God promised, they hit the road, and God took care of them. Also, he didn't know where he was going! Abraham relied completely on the revelation from God. He trusted God to take care of his household (i.e. small town).

All of Abraham's relatives didn't go either. This was contrary to culture. The family groups would stay together for protection. When families split up into smaller groups they became more vulnerable to marauders. Abraham left the protection of his father's house. He defied culture and believed God. He did God's Word and God prospered Abraham mightily after that.

:9 By faith he sojourned in the land of promise,
    as in a strange country,
    dwelling in tabernacles with Isaac and Jacob,
    the heirs with him of the same promise.
:10 For he looked for a city which hath foundations, 
    whose builder and maker is God.

Abraham was looking forward to God's promises; the messiah and the new Jerusalem.  A city in Abraham's time was built with walls all around. These walls were not meant to keep people in but to keep enemies, marauders out. They are there to protect the citizens of the city.  Abraham looked forward to the redemption of mankind and God's eternal protection.

:11 Through faith also Sara herself received strength to conceive seed,
    and was delivered of a child when she was past age,
    because she judged him faithful who had promised.

The New Revised Standard Version is a clearer translation.

Hebrews 11:11 By faith he received power of procreation
    even though he was too old
        -- and Sara herself was barren--
    because he considered him faithful who had promised.

:12 Therefore sprang there even of one, and him as good as dead,
    so many as the stars of the sky in multitude,
    and as the sand which is by the sea shore innumerable.
:13 These all died in faith, 
    not having received the promises,
    but having seen them afar off,
    and were persuaded of them,
    and embraced them,
    and confessed that they were strangers and pilgrims on the earth.

All of these people looked forward to the messiah, they embraced the promises, were persuaded, confessed the promises in all circumstances, i.e., Job "I know my redeemer liveth". They confessed that they were pilgrims, only passing through. They looked forward to the coming of the redeemer, the messiah, Jesus Christ. By faith, believing, we look forward to the return of Christ. We can embrace God's promises and live with power by believing.