You can say, Hi how are you? Then you can talk about the weather, eg Great day isn't it? or comment on a person's lovely watch.That's a beautiful watch you've got there. I need to buy a similar one. Can you tell me where you bought yours? Or a sporting event, eg Did you watch the match between X and Y last night. Great game wasn't it? The conversation should start to flow then.

An equivalent of "nice to meet you" is "pleased to meet you"; otherwise, there's the more formal "glad to meet you".

Thank you so much for answering my question. I understand it now. :) When I meet someone for the first time, i usually just say "Hi, my name's Kirsten. What was your name?" and then we start talking about whatever was going on. :)

"Nice to meet you" is probably the most common and easiest expression to use. You could also say something like "Its nice to finally meet you. I've heard so much about you." This is only used in situations where you have actually been told about the person. Be careful though, because that person might assume that you've heard bad things about them instead of good. :)

if you are introduced to someone you like you may say the french : "enchanté"