Usually 7-14 days. In the case of the Amazon gift card, I'm not entirely sure if they send you a physical card in the mail, but they give you an E-Code to redeem on Amazon's site once it is ready. It will tell you the code on the Order Status option of your profile/settings.
Well I've been on Swagbucks for about 3 weeks so far. With about 3-4 Hours of actual work spread over 3 weeks, I've been able to rack up 2 $5 Amazon cards and some more. Roughly 1000 points without offers. Here are some pointers to help you get some free money.
It only takes 450 points to earn...