Using some reflection and generics in two extension methods you can achieve that.
Right, others did mostly the same solution, but this uses less reflection which is more performance-wise and way more readable:
public static class ObjectExtensions
{
    public static T ToObject<T>(this IDictionary<string, object> source)
        where T : class, new()
    {
            var someObject = new T();
            var someObjectType = someObject.GetType();
            foreach (var item in source)
            {
                someObjectType
                         .GetProperty(item.Key)
                         .SetValue(someObject, item.Value, null);
            }
            return someObject;
    }
    public static IDictionary<string, object> AsDictionary(this object source, BindingFlags bindingAttr = BindingFlags.DeclaredOnly | BindingFlags.Public | BindingFlags.Instance)
    {
        return source.GetType().GetProperties(bindingAttr).ToDictionary
        (
            propInfo => propInfo.Name,
            propInfo => propInfo.GetValue(source, null)
        );
    }
}
class A
{
    public string Prop1
    {
        get;
        set;
    }
    public int Prop2
    {
        get;
        set;
    }
}
class Program
{
    static void Main(string[] args)
    {
        Dictionary<string, object> dictionary = new Dictionary<string, object>();
        dictionary.Add("Prop1", "hello world!");
        dictionary.Add("Prop2", 3893);
        A someObject = dictionary.ToObject<A>();
        IDictionary<string, object> objectBackToDictionary = someObject.AsDictionary();
    }
}