A Type 1 negative binomial distribution with parameters (k,p) can take the values k, k+1, k+2, ... (see Tables, page 8). A Type 2 negative binomial distribution with parameters (k,p) can take the values 0, 1, 2, ... (see Tables, page 9). So if you're not told which Type to use, ask yourself what values your random variable could take. If, for example, X is a random variable modelling "number of insurance claims incurred in December"; and you're told X is negative binomial, it will almost certainly be Type 2, because it's possible for no claims to occur.
