Here are some ornaments commonly used in whistle music.
A possibly clearer/alternative explanation on ornaments can be found at Brother Steve's tin whistle site.

Cuts and taps 

Cuts (above main note) and taps (below main note) are used widely in whistle music and usually one of the first ornaments to be learnt. They are similar to grace notes,  In classical music a grace notes duration is taken from the following  or preceding note but with a cuts and taps it's a bit less than that and shouldn't be thought of as taking time from the main note. It is a very quick finger movement which adds flavour to the line of music. For the initial cut on the first bar of the jig below, the cut will sound by lifting the second finger of the left hand (xox ooo) and putting it back quickly to make the G (xxx ooo) Practice just the first bar, firstly tonguing every note. So D, E, F# and cut the G... 

Here is the first part of a jig with some cuts, notice they can occur almost anywhere in the tune on or off the beat.

D whistle Garret Barry's

Taps

Taps or strikes are quick notes below the main note and like any "grace" note, very subtle. It's not very easy to show by notation. The notation below is the nearest I can get. Play the main note and gently tap the note below, it is difficult at first as the fingers either totally miss (because they are afraid of hitting too hard) or the note is hit too hard. The aim is somewhere in-between, which comes with persistent practice. Taps to me are easier on the bottom end of the whistle, the hardest being up the other end on B and A. They should all be practiced, the most difficult more frequently.

D whistle The Foggy Dew

Long Rolls

Rolls are probably the most sought after ornament on a whistle players need to learn list. They can be quite a challenge to get right but are worth the effort. The trick is, like anything, perseverance. Your cuts and taps should be pretty well practiced before attempting a roll.

The G long roll is about the easiest so we will start with that. The structure of the long roll is three main notes of the same pitch (see diagram). Between the first and second note there is a cut and between the second and third there is a tap. The first note is the most important and should be leaned on, the rest of the notes are just the ornamentation so should be thrown into the air as cleanly and lightly as possible.

Begin by taking the three notes G,G,G and playing them slowly, tonguing each one and counting one beat each, do that until the rhythm of three beats is established, then play the three notes as one, tonguing the first note and keeping the count of three going in your head, now add the cut and the tap and there you have it! Here is an example of a long roll on G. 

At first the fingers will probably flap all over the place either hitting the holes too hard or not reaching the hole at all, but as the saying goes... keep at it!

In the clip there are breath marks where I breathe more can be added as needed, as the tune becomes faster some could be dropped. In bar two the first group of three (G F# G) can be rolled...or not, as in the clip.

As I mentioned before a better explanation is at Brother Steve's tin whistle pages.

D whistle The Legacy Jig

Short Rolls

Next the short roll which is, as the name implies, a long roll with the first note omitted. This example is the short roll on F#. To achieve it, cut the first note simultaneously with the (F#). So keep the finger on the (F#) hole and cut the (A) note. As soon as the (A) finger is back on its hole tap the (E) note. 

An example of short rolls in a tune can be found on "Trip to Skye".

Short roll on F#

Christy Barry's

A good tune to practice all the above ornaments.

The clip is played the three ways, first the basic notes then with cuts and finally with a long roll and short rolls. Breathing places will vary with the tempo of the tune. I have inserted commas where mine are. Notice they are usually in the middle of a group of notes with the middle note omitted. In bar 6 the breath is taken after the crotchet (quarter note) so no note need be dropped there. In bar 7 of the last clip the quaver (eighth note) has been replaced by two semi quavers (sixteenth notes) to give a slight push.

D whistle Christy Barry's Jig

Trills

Trills are more common to the recorder and Baroque type music, used in the right places they can be effective in whistle music. They are not very easy to write down and in the example below they are written as semi quaver's but usually a trill will go faster. In the clip there are four slow beats to the bar. There are a couple in "Blind Mary" which is an ideal tune to practice them.

On the notes below start slowly with a metronome and only speed up when the notes are even and in time, use the upper octave too. Tongue the first note in each bar. This exercise can be a bit tedious but little and often...

Trills

Vibrato

Vibrato can be achieved two ways on the whistle, the more usual is finger vibrato. Another way is to use the diaphragm more commonly used in flute playing.

Finger vibrato

t = tap
x = closed hole
o = open hole

• For an example of vibrato on the note of G, the middle finger of the right hand should lightly tap the E note repeatedly (xxx oto). Two fingers can be used also (xxx ott}.
• On the A note the same applies either (xxo too) or (xxo tto).
• The B note would more usually be (xot ooo).
• C natural (oxx tto).
• C sharp (ott ooo).
• E (xxx xxt) the tap should just hit the side of the hole as if playing D# fingering.
• D well I don't know about that one! You could try this I suppose (txx xxx).
• F# (xxx xot)

Vibrato from the diaphragm

Used mostly by flute players in the classical idiom. The technique is to use the muscles of the diaphragm to gently push the air up in a pulse like action. It basically works by mouthing (ooh ooh ooh) and pushing from the diaphragm in a steady pulse. Initially practice blowing into the whistle at one pulse a second as you get the idea gradually increase the tempo...it's rather like turning a motor over, firstly a chugg and then a steady pulse. This takes quite a lot of practice to get the effect. Note that the pulse doesn't come from the throat as that would give a weak strangled effect.

Vibrato on G 

For a good all-round tone in whistle playing the breath should consciously come from the diaphragm and exit through a relaxed open throat. This is just a basic premise as the throat plays an important part in controlling the passing air. For instance the technique of throating or glottal stops which stops a note by using the glottis (the opening between the vocal cords). I haven't really learnt it myself so won't put on a clip.