Blood points are a simple concept, representing a sort of personal karma. Basically, if you whiff a roll, you earn a point. Later, you can spend a point to gain a +1 to a different die roll after the fact. If enough bad stuff happens to you, eventually something good happens.
Once on your own turn, whenever you roll a d20 and fail a roll for a power, a saving throw, or an ability or skill check, as an immediate reaction, choose one:
a) Earn a blood token. (I have red glass beads I give to players for tracking blood points.)
b) Spend one or more blood tokens. For each blood token you spend, gain +1 to your failed roll and reinterpret the roll to see if you succeed. You cannot turn a miss into a critical hit this way.
You do not earn blood points for rolls that have a “miss” effect.
Blood points never expire or go away, unless you spend them, though certain game effects might remove them (for example, a monster whose attacks remove blood points).
Redcap is asked to make a Diplomacy check. He rolls a 5, much lower than he needed to convince the dwarven residuum miners not to turn him in for snooping around. Redcap’s party members get nervous and start a fight. The failed roll earns him 1 blood point.
A few rounds into the combat, Redcap attacks with one of his sorcery powers, hoping to roll a 14. He rolls a 13, one short! Redcap spends his 1 blood point, changing the 13 to a 14, and turning the roll into a successful hit.
After a short rest, the party gets into the mines and ends up in a fight with a bunch of kobolds. Redcap has been rolling lousy all day, and he’s already earned 2 blood points (one missed attack and one failed saving throw). He casts a spell and misses by a wide margin, earning a third blood point. He spends an action point to try again. Another failure! He can’t earn another blood point for the miss, since he can only earn one per turn.
The next combat round, Redcap makes a really difficult attack roll (the opponent is at long range with cover and a high defense): he needs a 19 to hit. He rolls an 17. Redcap spends two of his three blood points to make the 17 into a 19. He could spend one more, but doing so will not make the hit into a critical hit, so he saves the blood point.