First apologies for that incorrect remark in the documentation. That's an outdated reference, we'll correct the docs a.s.a.p.
You have two options: if you want to have all string typed fields to be varchar, you can do that with one checkbox: Project -> Settings -> Conventions / Entity Model / Model First Development and uncheck 'Prefer natural character types'
If you want to have just a couple of fields to have a varchar db type, you should define a new type shortcut: Project -> Settings -> Conventions / Entity Model / Type Shortcuts.
In the top row of the grid type a new name for your typeshortcut, like 'vstring', specify the .net type as System.String and give it a default length. Press ctrl-enter to add the new row.
Select it, and you can then specify a preferred DB Type for this new type shortcut. Select SQL Server for the Database type, and as preferred DB Type 'varchar' and click OK.
Now in the entity editor (or quickmodel) you can use the 'vstring' type shortcut as the type for the field, instead of the 'string' type shortcut.
WHen you now sync the model using 'Sync Relational Model Data' the fields of type 'vstring' will be mapped onto varchar fields. Caveat: if they previously were mapped to nvarchar fields, the table fields won't be changed, as the designer doesn't see a necessity to change the target fields (as nvarchar is a valid target field for 'system.string'), hence the 'preferred db type'. To overcome this, on the mappings tab of the entity, select the field, click 'Edit field' in the bottom right corner to change the target field's type to varchar. You can then export a ddl sql script to apply that change to your database.