Most likely nothing special will be seen from Earth within the lifetime of the Sun. The most recent results (see discussion in Will Milky way and Andromeda collide for sure? ) suggests that the Milky Way and Andromeda will have an initial "glancing blow" with a pericentre (i.e. closest approach) of 75 kpc (220,000 light years) about 5 billion years in the future (van der Marel et al. 2019). They will then move apart and then later crash into each other again, before fully merging after about ten billion years in the future, when the Sun has long gone (Schiavi et al. 2020). in other words, the collision is not direct enough for anything spectacular to happen until the Sun has ended its life as a normal star in about 7 billion years time.
The radial extent of the discs of both galaxies is of order 15 kpc, with an exponentially decaying scale length around 3 kpc away from their centres. The Sun is only 8 kpc from the centre of the Milky Way. Hence, if the Milky Way and Andromeda have an initial closest approach of 75 kpc there will actually be very little direct interaction. In particular, there will be no merger of central black holes and no significant gas interactions within the lifetime of the Sun, since the gas is largely confined to a similar radial extent as the stars and the black holes are central.
The Sun itself would not be near the initial interaction region, so any increased star formation, supernovae etc. (which since the gas discs are barely interacting, I think would be modest), would be tens of kpc away. The local stellar density would barely be changed and the night sky would only look different in the sense of the Andromeda galaxy being around 75 kpc away. Astronomers however would be able to identify the Andromedean (?) stellar interlopers because of their strange velocity components (which would not be visible to the naked eye!) and slightly different chemical composition.
Having said all that, the error bars on the tangential relative velocity of the MW and Andromeda are still quite large. So although the above looks to be the most likely scenario, there is still a chance that the collision will be more direct. In which case I point you to Anders Sandberg's answer. Equally, it may still be possible that the interaction is even weaker and the MW and Andromeda will undergo a series of distant passes before merging on timescales of 50 billion years (Schiavi et al. 2020).
Small update:
The recent work of Salomon et al. (2021) updates the tangential relative velocity of Andromeda to $80 \pm 38$ km/s, a little bigger, but consistent with the $57 \pm 33$ km/s quoted by van der Marel et al. (2019).
A new paper by Schiavi et al. (2020) investigates the timing of the merger as a function of tangential velocity. For $v_t = 57$ km/s they find that the first closest approach takes place in 4.3 billion years at a pericentre of 50-100 kpc, depending on the density of the intergalactic medium, and the final merger takes place in 10 billion years - when the Sun will be a fading white dwarf.
The time of first close approach is only weakly dependent on the assumed value of $v_t$, but the time to merger is very dependent on $v_t$. Roughly, $\tau_{\rm merger} \propto v_t^5$ if there is no intergalactic medium, but is speeded up somewhat (unspecified in the paper, but seems to be doubled to 20 billion years for $v_t=92$ km/s from Fig.6 in the paper) by more realistic values.
The paper also shows that after the merger, the central black holes will coalesce on timescales of tens of million of years.
A further possibility, discussed by van der Marel et al. (2012) using $v_t = 30$ km/s (which is still within the bounds of possibility) has the merger at 6.5 billion years (when the Sun will still exist as a red giant). The merger has a $\sim 85$ per cent chance of making the Sun migrate to a larger radius from the merged galaxy centre. However, this would happen on long enough timescales that this isn't something that one would "notice" happening. But it is clear that the appearance of our galaxy would change from our present view of the Milky Way.