Scripture of focus: John 7:38
"He who believes in Me, as the Scripture said, 'From his innermost being will flow rivers of living water.'"

It is easy for us to say, "Yes, I believe", but what does "believe" actually mean? We can believe that the ocean is red at sunset, yet that is simply a condition of our viewpoint, not an actual truth. Therefore, believing requires an education, a choice, and a revelation.

The Greek defines believing as follows: 
4100 pisteúō (from 4102 /pístis, "faith," derived from 3982 /peíthō, "persuade, be persuaded") – believe (affirm, have confidence); used of persuading oneself (= human believing) and with the sacred significance of being persuaded by the Lord (= faith-believing). Only the context indicates whether 4100 /pisteúō ("believe") is self-serving (without sacred meaning), or the believing that leads to/proceeds from God's inbirthing of faith.

Once we believe, it is not enough to proclaim our faith. We must act upon it.
Believing - Faith connection: James 2
19You believe that God is one. You do well; the demons also believe, and shudder. 20But are you willing to recognize, you foolish fellow, that faith without works is useless? 21Was not Abraham our father justified by works when he offered up Isaac his son on the altar?22You see that faith was working with his works, and as a result of the works, faith was perfected; 23and the Scripture was fulfilled which says, "AND ABRAHAM BELIEVED GOD, AND IT WAS RECKONED TO HIM AS RIGHTEOUSNESS," and he was called the friend of God. 24You see that a man is justified by works and not by faith alone. 25In the same way, was not Rahab the harlot also justified by works when she received the messengers and sent them out by another way? 26For just as the body without [the] spirit is dead, so also faith without works is dead.

Not Believing:
Mark 16:16
11When they heard that He was alive and had been seen by her, they refused to believe it.

12After that, He appeared in a different form to two of them while they were walking along on their way to the country. 13They went away and reported it to the others, but they did not believe them either.

14Afterward He appeared to the eleven themselves as they were reclining [at the table]; and He reproached them for their unbelief and hardness of heart, because they had not believed those who had seen Him after He had risen. 15And He said to them, "Go into all the world and preach the gospel to all creation. 16"He who has believed and has been baptized shall be saved; but he who has disbelieved shall be condemned.

Cognate: 569 apistéō (from 571 /ápistos, "unfaithful," without faith, i.e. negating 4103 /pistós, "faithful") – properly, refusing to be persuaded by God ("betray His trust," J. Thayer).

569 /apistéō ("not willing to be persuaded") means more than "disbelieve" ("not believing") because it indicates "refusing to be faithful" (honor a trust or revelation from the Lord). See 571 (apistos).

569/apisteō ("refuse to be persuaded") is sin committed by believers(Mk 16:11; Lk 24:11,41) and unbelievers (Ac 28:24; Ro 3:3; 1 Pet 2:7). 569 (apistéō) reveals a person is unconvinced when they should be persuaded by what the Lord has done (offered).

Believing in Christ Defined in John 11:25
25Jesus said to her, "I am the resurrection and the life; he who believes (pisteuo) in Me will live even if he dies, 26and everyone who lives and believes in Me will never die. Do you believe this?" 27She said to Him, "Yes, Lord; I have believed that You are the Christ, the Son of God, [even] He who comes into the world."
 

Faith requires a Confession: Romans 10
8But what does it say? "THE WORD IS NEAR YOU, IN YOUR MOUTH AND IN YOUR HEART"-- that is, the word of faith which we are preaching, 9that if you confess with your mouth Jesus [as] Lord, and believe in your heart that God raised Him from the dead, you will be saved; 10for with the heart a person believes, resulting in righteousness, and with the mouth he confesses, resulting in salvation. 11For the Scripture says,"WHOEVER BELIEVES IN HIM WILL NOT BE DISAPPOINTED."

Confess:
3670 homologéō (from 3674 /homoú, "together" and 3004 /légō, "speak to a conclusion") – properly, to voice the same conclusion, i.e. agree ("confess"); to profess (confess) because in full agreement; to align with (endorse).

[3670 /homologéō ("confess") means to speak the same thing, i.e. "assent, agree with, confess, declare, admit" (Vine, Unger, White, NT, 120).]

Therefore we see that confession is an action that leads to a result. Believing is an inward choice, confession is an outward acknowledgement, and obedience is partaking in the plan of salvation: Repentence, Baptism, and receiving the Holy Spirit. 

Belief is Proven in Faith by Our Works Acts 8 - Ties into James 2:19
"And without faith it is impossible to please Him, for he who comes to God must believe that He is and that He is a rewarder of those who seek Him."