You can parse this string using a series of system expressions tokenat, replace, find, mid, left, right etc. See this link:
scirra.com/manual/126/system-expressions
For example, if you have a string {"token":"000000000000000000","privatetoken":"1111111111111111111111111111"} in variable Var and you need to extract the privatetoken value, you can do this:
// first remove all characters {, } and " from the string
Set Var to replace(Var, "{", "")
Set Var to replace(Var, "}", "")
Set Var to replace(Var, """", "")
// then extract the provatetoken value
Set Var to tokenat(Var, 1, ",")
Set Var to tokenat(Var, 1, ":")