I know that a player in my squad is indicated in-game with a green name, but I would like to know if my other teammates are also in a squad or are solo.
That would be helpful for team communication and for coordinating attacks.
As of today's patch, a visual indicator of whether or not players are in a party are shown in the scoreboard menu:
When the players are in a party, you'll see a link between the party members within the party. In this screenshot, the enemy team has two parties, a party of 2 and a party of 3.
Before the game starts, you could just ask the people in your Team if there are any premades in the game. Being premade with other players means to be in a party/group with them to play together.
Most of the times, people will tell :)
Currently there is no labeling or way to tell if other team mates or enemy teams are part of a premade. Here is a post on the matter. One suggestion would be to keep an eye out for multiples of people joining a match at the same time, although I'm not sure how accurate that is.
Update: As waifu says, grouped players are now indicated on the scoreboard by links between character portraits. The following still applies however.
Groups are in group voice chat by default and must join team voice chat manually. If they join team voice chat, they remain there until requeuing.
Please join team voice chat if you're in a group.