You can use the substringWithRange method. It takes a start and end String.Index.
var str = "Hello, playground"
str.substringWithRange(Range<String.Index>(start: str.startIndex, end: str.endIndex)) //"Hello, playground"
To change the start and end index, use advancedBy(n).
var str = "Hello, playground"
str.substringWithRange(Range<String.Index>(start: str.startIndex.advancedBy(2), end: str.endIndex.advancedBy(-1))) //"llo, playgroun"
You can also still use the NSString method with NSRange, but you have to make sure you are using an NSString like this:
let myNSString = str as NSString
myNSString.substringWithRange(NSRange(location: 0, length: 3))
Note: as JanX2 mentioned, this second method is not safe with unicode strings.
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