How do I seed a random class to avoid getting duplicate random values

A good seed generation for me is:

Random rand = new Random(Guid.NewGuid().GetHashCode());

It is very random. The seed is always different because the seed is also random generated.

Bit late, but the implementation used by System.Random is Environment.TickCount:

public Random() 
  : this(Environment.TickCount) {
}

This avoids having to cast DateTime.UtcNow.Ticks from a long, which is risky anyway as it doesn't represent ticks since system start, but "the number of 100-nanosecond intervals that have elapsed since 12:00:00 midnight, January 1, 0001 (0:00:00 UTC on January 1, 0001, in the Gregorian calendar)".

Was looking for a good integer seed for the TestApi's StringFactory.GenerateRandomString

You should not create a new Random instance in a loop. Try something like:

var rnd = new Random();
for(int i = 0; i < 100; ++i) 
   Console.WriteLine(rnd.Next(1, 100));

The sequence of random numbers generated by a single Random instance is supposed to be uniformly distributed. By creating a new Random instance for every random number in quick successions, you are likely to seed them with identical values and have them generate identical random numbers. Of course, in this case, the generated sequence will be far from uniform distribution.

For the sake of completeness, if you really need to reseed a Random, you'll create a new instance of Random with the new seed:

rnd = new Random(newSeed);

In case you can't for some reason use the same Random again and again, try initializing it with something that changes all the time, like the time itself.

new Random(new System.DateTime().Millisecond).Next();

Remember this is bad practice though.

EDIT: The default constructor already takes its seed from the clock, and probably better than we would. Quoting from MSDN:

Random() : Initializes a new instance of the Random class, using a time-dependent default seed value.

The code below is probably your best option:

new Random().Next();