How does the double strike effect workin magic?

Answer 1

A creature with Double Strike deals both first strike and normal combat damage. so in total it deals double its normal damage.
some examples:
if a 2/2 creature with double strike blocks a 4/4 creature they would both receive 4 damage and die.
if a 2/2 creature with double strike blocks a 2/2 creature the creature with double strike deals its damage before the creature without, so only the creature without double strike dies.
if a 2/2 creature with double strike blocks a 2/2 creature with first strike they would both deal 2 damage to each other in first strike step so both die.
if a 1/2 creature with double strike blocks another 1/2 creature with double strike they deal a total of 2 damage to each other so both die.

if a creature with double strike is blocked it won't deal damage to defending player (unless it has trample) even if the blocking creature is destroyed or exiled.

Official magic the gathering rules:

http:/rules.wizards.com/rulebook.aspx?game=Magic&category=Game+Rules

"502.28. Double Strike

502.28a. Double strike is a static ability that modifies the rules for the combat damage step. (See rule 310, "Combat Damage Step.")

502.28b. At the start of the combat damage step, if at least one attacking or blocking creature has double strike or first strike, creatures without double strike or first strike (see rule 502.2, "First Strike") don't assign combat damage. Instead of proceeding to end of combat, the phase gets a second combat damage step to handle the remaining creatures. In the second combat damage step, surviving attackers and blockers that didn't assign combat damage in the first step, plus any creatures with double strike, assign their combat damage.

502.28c. Removing double strike from a creature during the first combat damage step will stop it from assigning combat damage in the second combat damage step.

502.28d. Giving double strike to a creature with first strike after it has already put first strike combat damage onto the stack in the first combat damage step will allow the creature to assign combat damage in the second combat damage step.

502.28e. Multiple instances of double strike on the same creature are redundant. "

Answer 2

With Double Strike and First Strike, an extra damage step is added before the normal one. In this extra step, Double Strike and First Strike creatures deal their damage to the appropriate blocking creatures. If it's lethal damage, state-based effects apply and it dies before the next damage step. Then the next damage step begins. All creatures except First Strike creatures would now deal their damage to the opposing creatures.