There are a few methods which are used for voting at a meeting. The most common is the chair asking all those in favour to please signify by saying aye and contrary minded to signify by saying nay. However, if the matter being voted on is contentious this may not be the best way to vote. If there are participants who are timid, they may be reluctant to cast their vote in public, if they feel others will disagree. Hopefully your group does not have any bullies, but there could be some lobbying going on.
The best way to deal with a contentious decision may be the secret ballot. All you need is a few scraps of paper and a hat or a bowl. If you want a decision which is made without concern about how others are voting, then the secret ballot is the way to go. After all, this is how we cast our ballots in elections here in Canada.