If you don't want to add the MoreLinq library to your project just to get the DistinctBy functionality then you can get the same end result using the overload of Linq's Distinct method that takes in an IEqualityComparer argument.
You begin by creating a generic custom equality comparer class that uses lambda syntax to perform custom comparison of two instances of a generic class:
public class CustomEqualityComparer<T> : IEqualityComparer<T>
{
    Func<T, T, bool> _comparison;
    Func<T, int> _hashCodeFactory;
    public CustomEqualityComparer(Func<T, T, bool> comparison, Func<T, int> hashCodeFactory)
    {
        _comparison = comparison;
        _hashCodeFactory = hashCodeFactory;
    }
    public bool Equals(T x, T y)
    {
        return _comparison(x, y);
    }
    public int GetHashCode(T obj)
    {
        return _hashCodeFactory(obj);
    }
}
Then in your main code you use it like so:
Func<Person, Person, bool> areEqual = (p1, p2) => int.Equals(p1.Id, p2.Id);
Func<Person, int> getHashCode = (p) => p.Id.GetHashCode();
var query = people.Distinct(new CustomEqualityComparer<Person>(areEqual, getHashCode));
Voila!  :)
The above assumes the following:
- Property Person.Idis of typeint
- The peoplecollection does not contain any null elements
If the collection could contain nulls then simply rewrite the lambdas to check for null, e.g.:
Func<Person, Person, bool> areEqual = (p1, p2) => 
{
    return (p1 != null && p2 != null) ? int.Equals(p1.Id, p2.Id) : false;
};
EDIT
This approach is similar to the one in Vladimir Nesterovsky's answer but simpler. 
It is also similar to the one in Joel's answer but allows for complex comparison logic involving multiple properties. 
However, if your objects can only ever differ by Id then another user gave the correct answer that all you need to do is override the default implementations of GetHashCode() and Equals() in your Person class and then just use the out-of-the-box Distinct() method of Linq to filter out any duplicates.