The best way to learn is to listen to a lot of ITM recordings! There are many collections and individual CDs of tinwhistle recordings.
Everyone develops their own style in time, but a few suggestions.
When you get two consecutive notes of the same pitch, separate with a cut or tap.
On a dotted crotchet in a jig, you can do a long roll, or a triple tongue (sometimes called a treble).
On a crotchet, a short roll will fit. In a Reel a triple tongue would fit.
When going up to a top note, you can cut above and come down to it.
Similarly when dropping to a low note, tap below and come up to it.
Don’t be tonguing every single note! Tongue some and slur some. On fiddle, I would usually follow a crotchet with two slurred quavers. In a reel or hornpipe, where a bar contains 8 full quavers a pattern of 1 2 3 (456) 7 8 with 456 slurred is useful. An alternate is 1 (234) 5 6 7 8. On a whistle you’d probably slur more than this.
In polkas, a slide can sound good, say if you have an “e f#” pair of quavers. try sliding from the e to the f#.
Just a few ideas. The most useful and natural for me is the cut, I almost always cut rather than tongue or change bow stroke on two consecutive notes of the same pitch and length. You’ll see this a lot in Irish jigs.
Which finger to cut with? Some people teach a cut with the upper ring finger, but this only works up to a point. Brian Finnegan always cust with the top first finger. After all it’s down the most, and a cut is really a blip of sound and not a true note.
Oh, and don’t over do the ornaments. Too many is often worse than none at all.