As said above to transpose from Concert pitch to an Eb instrument, you add 3 sharps. then shift notes accordingly, but the key signature always should have 3 extra sharps.
But I look at it this way - if my instrument is an Eb pitched instrument, when I play a written C, it sounds Eb, so I write out the scale of C major and call this "written Sax in Eb", then immediately underneath it, I write out the scale of Eb major and call this "sound like, Concert pitch"
then I use this "ready reckoner" as my crib for transposing from C to Eb.
I use this method for any transposing instrument.
You might need to check a little more as to exactly where you need to pitch your new note (eg is it a D under the stave or a D on the 4th line) but it should be fairly self- obvious anyway.
Great! Thank you so much