For types known at compile-time, use a generic parameter with Query<T>.

public class Dog
{
    public int? Age { get; set; }
    public Guid Id { get; set; }
    public string Name { get; set; }
    public float? Weight { get; set; }

    public int IgnoredProperty { get { return 1; } }
}    

//
IDBConnection db = /* ... */;

var @params = new { age = 3 };
var sql = "SELECT * FROM dbo.Dogs WHERE Age = @age";

IEnumerable<Dog> dogs = db.Query<Dog>(sql, @params);

You can also query dynamically if you leave off the generic type.

IDBConnection db = /* ... */;
IEnumerable<dynamic> result = db.Query("SELECT 1 as A, 2 as B");

var first = result.First();
int a = (int)first.A; // 1
int b = (int)first.B; // 2

var color = "Black";
var age = 4;

var query = "Select * from Cats where Color = :Color and Age > :Age";
var dynamicParameters = new DynamicParameters();
dynamicParameters.Add("Color", color);
dynamicParameters.Add("Age", age);

using (var connection = new SqlConnection(/* Your Connection String Here */))
{
    IEnumerable<dynamic> results = connection.Query(query, dynamicParameters);
}