How long does it take for Google Analytics Goals to start show some data?

You can see goals appear instantly in the Real Time Conversions report.

One other thing to bear in mind when testing: make sure you aren't filtering out your IP address as you won't see any results from testing.

It can take 24 - 48 hours to show up in the standard reports (Conversions -> Goals -> ...)

Data processing latency

Processing latency is 24-48 hours. Standard accounts that send more than 200,000 visits per day to Google Analytics will result in the reports being refreshed only once a day. This can delay updates to reports and metrics for up to two days. To restore intra-day processing, reduce the number of visits you send to < 200,000 per day. For Premium accounts, this limit is extended to 2 billion hits per month.

Basic Goal Data can be found almost instantly in the Real-time -> Conversions report