A vote of no confidence in the town council will not actually have any specific result, although it may influence some councillors. I have experienced a situation where continuing public pressure brought about resignations, followed by a poll that elected councillors with different views.
Members of the public cannot force any motion to be discussed by the council. However, what you can do is to call a town meeting. This normally occurs once a year, but six members of the public can demand an additional town meeting. All electors are entitled to attend. A town meeting can debate motions and vote on them, but in most cases the result is not binding on the council. It can have an impact, though, especially as part of a campaign.