You should start out by givign the wrapper your login details. If emulating a technician, then pass their login details here. If making a service then pass in the details of your "service account technician" instead.
TrackIt_2019.API.BaseUri = "https://YourTrackItServer/TrackIt/WebAPI/";
TrackIt_2019.API.Authentication.Username = "UsernameForTrackitLogon";
TrackIt_2019.API.Authentication.Password = "password";
TrackIt_2019.API.Authentication.Group = "Group that this user is part of";
The return from the Delete(int ID) method is a boolean representing success/fail of the deletion. Everything else returns a dynamic (ExpandoObject) representing the object you are working on. So a Get(int ID) and an Assign(int ID, string TechnicianLogin) will both return an object with the properties of a ticket.
TODO :: Make strongly-typed objects to reflect the returns from the API (ticket, assignment, note)
To get Ticket # 78452 into the variable foundTicket
dynamic foundTicket = TrackIt_2019.API.Ticket.Get(78452);
To assign that ticket to the technician with login "JOHN-DOE" (note: here I assign the ticket but discard the object that is returned)
TrackIt_2019.API.Ticket.Assign(foundTicket.TicketID, "JOHN-DOE");
There are enumerations created in the Enum.cs file. I've included a handful, but your setup may not actually have all of these. At the underlying end TrackIt is actually looking for/using strings. I just put together the Enums so that I could reference something that already had all of the strings (that I commonly needed). Feel free to add/remove/change the enums packaged here to more closely match your implementation.
TODO :: Actual documentation of the methods. Most are rather self-explainatory, but docs > no-docs.