Like the other posters said, introvert simply means you get your energy back by doing things alone and extroverts get it from being around others.
How long will it take? It all depends on how determined you are to overcome shyness, low self esteem and become comfortable with yourself. I was shy growing up, stuttered pretty badly in social situations. It took me about 4 years before I became completely comfortable talking to anyone.
Here's an overview of how I did it. I more or less took on one stage before moving onto the next. At each step there was a fear to overcome. After the first dozen or so times doing each stage I became comfortable with it.
1. Saying hi to random strangers
2. Starting small talk to with strangers
3. Revealing more about myself in conversations
4. Going to party/bars and saying hi/introducing myself to EVERYONE I saw
5. Introducing myself to everyone I saw during the day-much more difficult than a party or a bar
6. Becoming vulnerable in social situations. The essence of "cool" is having no social boundaries or being reserved at all. You make jokes that might not be funny but you don't care. Saying things that might not agree with the rest of the pack.
7. After a few times of being disliked for being vulnerable and honest I became comfortable with people not liking me which led to more people liking me.
8. Learning
how to love and appreciate myself
With getting to a point where I actually enjoyed having conversations was mostly a mental thing. I (most likely you too) am very smart person but also introverted. I was frustrated at my lack of social skills and instead of doing something about it I rationalized it. I came up with beliefs like "people are so stupid, what's the point of talking to them?"
I would find fault with people who had what I didn't to feel superior for my own feelings of inferiority. Underneath those cop outs was a strong fear. This might be what's going on with you. Take time to think of what your beliefs are about other people and being social. Being aware of the outdated beliefs that you carry around with you will help you heal some wounds.
Keep at it. One of the best moments you can have is when you realize you have obtained the skill and can CHOOSE whether or not you want to be social. At that moment you feel empowered instead of victim to your circumstances.
DON'T read up on How to Be Social. It's a skilled that is learned through trial and error. Teaching someone how to be social (do this hear, say this in that situation) is similar to teaching someone how to ride a bike-I can teach you the basics but you only truly learn by hoping on that bike and falling down a lot.
Another aspect that you realize after you hit the moment where you have choice is that not every bad conversation is your fault. People are vastly different and you won't be able to connect and converse with all of them.
For example, I'm into personal development, relationships, dating, so me and you would probably hit it off in a conversation. On the other hand, if you were into sports and sports alone there would be dead air.