How to streamline userform coding for faster run time.

Usually when there are efficiency issues the first place I look are loops. You do not have any loops in your code.

On my laptop the form runs fine, but when I place it on the operators computer; it is laggy and slow

I suspect this says more about the operator's computer than your code. Do you know the specs of the computer?

By the way the indentation in this code is a bit eccentric, making it difficult to read. I also recommend you rework your code to get rid of the GoTo statements. That is probably not causing your issue but is a poor coding practice. Here is a rewrite of one of your subs.

Private Sub savecmd_Click2()

   'The bottom 4 if statements are to check for blank answers
   If TallySheet.carrier.Value = "" Then
      Dim carriermsg As VbMsgBoxResult
      carriermsg = MsgBox("Enter Carrier Number", vbOKOnly)
      Me.carrier.SetFocus
   Else
      If TallySheet.carrier.Value > 100 Then
         carriermsg = MsgBox("Enter Valid Carrier Number", vbOKOnly)
         Me.carrier.SetFocus
      Else
      
         'Check if color was marked
         If Not TallySheet.black.Value And Not TallySheet.ngrey.Value And Not TallySheet.red.Value Then
            Dim colormsg As VbMsgBoxResult
            colormsg = MsgBox("Select Color", vbOKOnly)
            Exit Sub ' instead of exiting sub, shouldn't you continue and check size?
         End If
         
     
         'Check if size was marked
         If Not TallySheet.lbr.Value And Not TallySheet.small.Value And Not TallySheet.medium.Value And Not TallySheet.large.Value Then
            Dim sizemsg As VbMsgBoxResult
            sizemsg = MsgBox("Select Size", vbOKOnly)
            Exit Sub
         End If
      
Part:
         If TallySheet.partnum.Value = "" Then
            Dim partmsg As VbMsgBoxResult
            partmsg = MsgBox("Enter Part Number", vbOKOnly)
            Me.partnum.SetFocus
            ' no need to exit sub here, it's the last code that will execute anyway
         Else
            Dim savemsg As VbMsgBoxResult
            savemsg = MsgBox("Information saved.", vbOKOnly)
            Call save
            Call clear
            Me.carrier.SetFocus
         End If
      
      End If
   
   End If
   
End Sub

The Call statement is obsolete and retained for backwards compatibility. It is not required to call a sub. You can just use the name of the sub.

Originally Posted by paintman

Also for the call functions all I would need to do is type "Save" or "Clear" to call the function?

Yes but I'm a little concerned about having a Sub named Save since that is also a method of Workbook. If what you have works I wouldn't remove the Call.

Originally Posted by 6StringJazzer

If what you have works I wouldn't remove the Call.

There will be no difference either way. It would be better to rename the routine though, IMO.

Originally Posted by 6StringJazzer

...The Call statement is obsolete... You can just use the name of the sub.

One small proviso: if you need to pass parameters to the called sub or function, the two methods vary slightly.
CALL MyFunction(a, b) requires parenthesis
vs.
MyFunction a, b no parenthesis... unless you're using the return value
vs.
t = MyFunction(a, b)