All of the information in this post is taken from the Q&A and rulebook pages on the official Japanese Battle Spirits website.
1) the basics of Braves
2) summoning rules of Braves
3) Effects of Braves
4) Remaining Braves
I am making this post to help all those players out there who do not fully understand how braves function. A brave card is different from a spirit card.
1) It has a color, cost, and sometimes reduction the same as a spirit but they are much different. What a brave can do is combine with a spirit/ultimate that meets the correct brave condition specified on the card. For example, on balgunner his brave condition is a cost 4 or higher spirit, Sieg-apollodragon fits that condition thus you can brave it to him. When you brave a card that braves cost, color, symbols, are added to the spirit/ultimate it is braved to and then increases that cards bp at all of it's levels by the number specified in the brave effect section (under the red line) In the case of Sieg, braved to balgunner he would be a cost 10 double symbol red spirit in the astral dragon family with an extra 2000BP at all three of his levels.
2) When summoning a brave card, you can first summon it in spirit condition, by placing core on it then it is treated as a spirit and anything that effects spirits also effect them, you cannot brave a spirit condition brave (there is one card that is the exception to this rule though)
Or, if you have a spirit/ultimate that fits the brave condition already on the field when you are summoning the brave card you may directly place the brave onto that card and brave it.
3) Braves can have the same when attack/block and/or when battle effects that same as spirits/ultimates. Most are active after it is braved, in which case the effect shall activate during the correct timing, and if you spirit/ultimate has an effect that activates at that same time as the controlling player you select the order in which those effects activate. For example Sieg and balgunner, balgunner's when braved effect activates when the brave spirit attacks, likewise Sieg has two effects that activate when he attacks (the first being active at any level and the second being active when he is braved at level 3) so you may choose and select the order in which those effect go off.
4) When a brave spirit/ultimate leaves the field (either by destruction, depletion, or being returned to the hand/deck) the brave card may remain on the field in the same position (refreshed or exhausted) that the brave spirit was in by adding any number of cores you want onto it. Or, you may have the brave follow the spirit/ultimate to whenever it is going. If the brave spirit/ultimate would leave the field while it is attacking/blocking before BP is compared and you decided to leave the brave on the field then the attack/block shall continue with the brave.
If you have any further questions please do not hesitate to make a reply down below and either myself or someone else will get back to you.