In all probability, you can't do that, or not without a lot of work to create a generic routine.
The table name is no problem: just insert it into your SQL INSERT statement:
Dim sqlCommand as String = "INSERT INTO " & tableName & "...
The problem comes with the actual table data itself.
Unless you know exactly what the table holds, there is a very good chance that the insert will fail: because you are trying to be generic about this, you can't list the columns that you are going to insert, so you don't know how many rows worth of data you are trying to insert. Since the SQL INSERT statement is row based, this becomes a real problem.
In addition, if any of your columns are Identity fields, you cannot supply a value for them so you have to explicitly name the fields you do wish to load in the INSERT statement (and it's considered good practice to do so anyway).
To be honest, I wouldn't do it - just use a DL that "knows" about the database structure and save data that way instead.