It would probably be it's value and function. Some altcoins do not have a relevant function and just been generated in order to overthrow bitcoin. I trust an altcoin that is functional and has the potential to last for years. Also, the fact that the altcoin would be demanded by a lot of people gives me a sense of confidence that the altcoin is not just a worthless coin.

first define trust?
what are you looking for? do you mean as an investment or as a currency to use?
it is usually an investment so is it ICO or just a simple trading?
and remember that you are not trusting with your life it is just an investment that you make temporarily and pull out as soon as you can.

yes thats important is to trust the new altcoin but make sure that you read all the information about this altcoin so you can trust it. because
every new altcoins is the beginning of the future altcoins so thats why we trust it.

For me I see other people's belief in the altcoin with me reading their feedback, altcoin growth, good respond from altcoin, and developments made by developers. It's my opinion and just a suggestion from me, because I'm still learning still need more knowledge.

For me to trust a new altcoin, i will look at the various factors and aspects of the project to see if they are legit or be successful. The team, whitepaper, goal, other serious factors are to be heard with first, if i find it suiting enough for me then i'll give it a shot.

A new altcoin will need to prove its worth and its use to the community and society. It needs to be real, and has to be practical and useful. This new coin will need to have a team of devs that are willing and able to support and maintain it constantly for it to work in the world.

So true because there are some that are just good when it started but in the end they'll just leave you hang in the air. Having a solid team is a must for me because they're the one who really act first and being a front liner in this business is something to look for.

First you need to look at the project. What it is, who will need it, and whether such a project is necessary to anyone at all. The second step is to view the developers. What leadership and what kind of team. If all is good then you can take, but then again, it's not a fact that this company will have everything as planned by the developers!

Doing a research on the background of the team if either they have not been in to scamming. Looking in to their webpage for important information that might help you choose it. Checking the project if it is reliable at the same time the projects their running are existing. Give them  couple of question of this and that if they can answer your question properly. These simple thing gives much for you to help choose and trust new altcoin.

1) The team. This is very important! You have to look at their profiles, their background, their linkedin, twitter, everyone. You have to "pre-trust" them.

2) Forums and blogs. See what others are saying about it (that is, apart from bounty campaigners)