I read somewhere that the Sun, and its attendant planets, and other 'bits and bobs', orbits the centre of the Galaxy (taking many thousands of years to complete a full orbit). The Sun is roughly 30 thousand light years from the Galactic centre and about 20,000 light years from the edge (the Galaxy being about 100,000 light years in diameter).

The Sun itself is thought to be in the centre of a vast and diffuse 'shell' of icy material called the 'Oort Cloud'. The Sun's orbit around the Galactic centre is, more or less, in the same plane as the Galactic disc - but as it moves through its orbit it tends to 'wobble' up and down, passing periodically through volumes of space with slightly different amounts of matter in them. This motion sometims acts to dislodge icy lumps from the Oort cloud - which then fall in towards the Sun becoming comets (a comet's tail is caused by material boiling off from the icy lump's surface as it gets closer to the Sun).

I would guess that one of the first things we would notice about a collision between our Galaxy and Andromeda would be an increased number of comets as the disruption displaces more matter from the Oort Cloud.

But we probably won't be around by then to notice anything at all!