Introductions and such are important and all, but I have seen many many people who stick to an introduction script, which will suddenly drop off.
Hello. How are you? I'm ----. Nice to meet you. .... .... (awkward silence)
If you're meeting someone casually then it's important to immediately turn that introduction into a conversation. Say something about yourself or about the person. Sometimes this is natural in our own language, but we're so busy trying to think in another language or waiting for the native speaker to say something that we don't think to take charge of the conversation ourselves.
Definitely, inject your personality into your introduction. After all, that's what an introduction is all about - showing who you are! Tell them what you do. Ask them if they enjoy doing something that you like; "Do you play tennis?" If they say yes, instant conversation and will greatly increase the person's interest in you.
Try to be observant. If most of your English is standard conversational things, it wouldn't hurt to learn specific English terms regarding subjects you enjoy so that you can hold a conversation about that thing in English. If there is something you know a lot about in your own language, try to learn about it in English. After all, how can you be who you are if you can't talk in any detail about things you enjoy? If you can't do these things, to someone who can't speak your language you might just seem like a very blank person.