One of the most important concepts when you are trying to go from an introvert to an ambivert is the idea that you need to start conversations. You need to break the ice.
Introverts are usually so much in their head that they overthink things and then when the opportunity presents itself to break that ice they can't do it because they are worried that they will say something wrong or offend the other person. Rather than take the risk and start a conversation they won't do anything and the opportunity is gone.
Extroverts on the hand will start a conversation and because it is second nature to them they don't really care if the other person doesn't really take to them because they know that someone else will if they open a conversation with enough people.
How do you start a conversation with a stranger?
Well the secret is in the power of observation. I'll give you an example.
I was near a major university in Tokyo the other day walking towards the train station. In front of me I noticed a woman carrying a bag. The design on the bag was one I was very familiar with. So I broke the ice,
"Hello. Do you play cricket?" (The woman was carrying a cricket bat.)
Initially she was taken aback for a couple of seconds but then she told me that yes she did play cricket and although our conversation was less than a minute it was obvious that she was very enthusiastic about the sport and even though she had only played for less than 18 months she seemed to know all the jargon and things associated with the sport.
How did I get into this conversation?
I noticed something about her that I was familiar with and I commented on it. Basic, right? People will talk about something that is relevant to them.
In New Zealand, especially in supermarkets, cashiers will ask you generic questions about your day but if they were taught to use their observation skills then the customer would have a better experience.
I used to work as a bartender and some of the better interactions I had with customers was when I would comment on something that they were wearing or carrying or even something they just said.
If you want to start a conversation, look for something and comment on it. You might not be successful every time but you will build your conversation starter "muscle" and be well on the way to becoming an ambivert.