If a creature has a blocker assigned to it during the declare blockers step of combat, no damage will go to the player. This is true even if the blocking creature is no longer on the battlefield. For example, a player could have a creature block, then Unsummon it back to his/her hand. The attacking creature still had a blocker assigned to it though, so the damage will not go to the player. In your example, the blocking creature will die during first strike combat damage, but since the attacker was blocked, the normal combat damage will not hit the player.
The exception to all of this is if the attacking creature has trample.
double strike is two fold. 1.first strike damage 2.regular combat damage. if it is unblocked it deals both first strike and regular combat damage to the player. if blocked by a vanilla creature, a 2/2 doublestriker vs. a 2/2 vanilla, the vanilla creature will die to the 2 points of first strike damage and the doublestriker will not deal regular combat damage because 1. the blocker is already dead and 2. the doublestriker is already blocked therefor cannot deal damage to the player. if a 2/2 doublestrike is blocked by a 3/3 vanilla creature the 2/2 DS will deal first strike to the creature but the 3/3 V will survive and they will both deal regular combat damage to each other resulting in both creatures dying because the 3/3 has been dealt a total of 4 damage (2 first strike and 2 regular combat damage) and hits the 2/2 DS with 3 regular combat damage points.
things get more complicated when additional keywords and abilities come into play ie; deathtouch, trample, infect, wither, lifelink or any abilities that trigger when the creature deals damage to creatures or players. especially if the blocking creature has any of these abilities including doublestrike or first strike.