There are many solutions out there. You will find many on your very first search. But here is a simple solution that I have used in past. Maybe it can help you. What I am going to do is show dropdownlist from Enum and back to binding enum on bind model as selected.
Models:
public enum UserDocumentType
{
    IdCard,
    Passport,
    DrivingLicense,
    ResidentsPermit
}
public class SampleViewModel
{
    public UserDocumentType DocType
    {
        get;
        set;
    }
}
Controller:
public ActionResult Index()
{
    //Select default as Passport
    var user = new SampleViewModel
    {
        DocType = UserDocumentType.Passport
    };
    return View(user);
}
public void Submit(SampleViewModel vm)
{
    //vm.DocType would be what was selected when submit was clicked
}
View:
    <form action="@Url.Action("Submit")" method="post">
        @Html.DropDownList("DocType", 
        Enum.GetNames(typeof(HelloWorldMvcApp.UserDocumentType)).Select(n => new SelectListItem { Text = n, Value = n, Selected = n == Enum.GetName(typeof(HelloWorldMvcApp.UserDocumentType), Model.DocType) }))
        <input type="submit" name="Submit" value="Submit" />
    </form>
Here is an executable you can run or copy into your solution and try out: https://dotnetfiddle.net/DXCcHp