Some people make friends easily and effortlessly break the ice with strangers. Others do not.
It is for this last group that line dancing can change everything - you just get up and join in.
Learning a few line dances is easily done on your own.
And they aren't just for a row of grannies
- they're good fun for everyone.
Here's an example.
(For the full video see Youtube: Cotton Eye Joe Dance by DJ Raphi).

In case you didn't learn them from the video, here are the steps:
Tap right heel forward twice.
Tap right toe backward twice.
Right leg to the side, the up behind the left leg and touch the heel with the left hand.
Swing the right leg in front of the left leg and touch the heel with the left hand.
(Or, if you prefer, touch twice behind, and next time twice in front.)
Sidestep twice to the right, then twice to the left.
Do it all again but mirror image to the left.

Instead of just side stepping, when you're bringing your foot alongside, bring it behind the other foot. This is called the 'grapevine', and it looks good.
Also, instead of sidestepping/grapevining, you can turn around (but still moving right or left). This is usually done when moving to the left.
See Urban Cowboy Line Dancing: Cotton Eye Joe beginner line dance lesson with Kyle (Modern Version).

For steps and videos of a stack of line dances, see Copperknob stepsheets.
Though it's called 'Line Dancing' there's no compunction to dance in a line.

At the moment the most popular line dance seems to be 'The Electric Slide'. The steps are:
Grapevine twice right. Grapevine twice left.
Three steps back.
Left foot forward and rock body forward.
Swing right foot round so the body makes a quarter left turn.
Move the left leg behind the right, starting the grapevine to the right and do everything again.
- See Superlinedance: Electric Slide Line Dance.