Inner Game is a gigantic subject and can not be covered in one post. I will try to cover as much as possible and talk about my experience. I will try to recommend what can be done to improve if one is having problems. Please note, these are only my opinions based on my experience. I am not a psychologist, just someone who has been dealing with this (and still is at some degree).

I was a shy person. I was (and still catch myself) thinking "what if" questions. "What if I accidentally offend someone?", "What if I accidentally hurt someone?", "What if I make a wrong decision?", "What if..." Don't get me wrong, going always head first is an idiotic behavior, but finding that fine line can be a trick.
I was raised to be polite and not to insult anyone. I always listened to my parents. I was a "good" kid everyone was talking about and proud of. I was protected by a bubble of goodness and didn't see how world was in reality. "If I were good to others, others will be good to me." Unfortunately that is not always the case. Polite raising resulted in me not being a fighter and very insecure person. I kept my insecurities by playing safe and overachieving. I wasn't going to any competitive events (because I might loose). "What would people think about me then?"
First step is admitting you have a problem (alcoholics anonymous ftw). Then committing (not deciding, commuting) to do something about it. Changing yourself is extremely hard but rewards are unimaginable.

One of the "early things" came to me when I started working during my high school years. I was a promotional event organizer for one marketing company. Organizing an event is no problem (you have to have a good checklist). Running an event and leading the staff is another thing. It started as organizing a small 10, 20, 30 person events. I was managing a crew consisting of myself and my laptop. Easy. Right? Not exactly. Working with people is hard and it is very difficult to please everybody (e.g. impossible). Someone will always complain. I spent countless hour sobbing to one of my best friends about how "nobody likes me". When I finally realized I don't need to please everybody (and I can't no matter how much I want to) I started dealing with my insecurities (still a long way, though).

First "axiom" I started living by is "It is not important what is someone saying, but who is saying it".
Don't bother with random people's opinions and thoughts about you and yourself. Bother about opinions and thoughts from those closest to you. They care about you and they will set you straight. Try it, it works wonders. I heard about it but didn't took it seriously until I decided to change myself. If I did I could have saved myself a lot of pain. But there is no school like life.

Another eye opener came from that same high school job. I was supposed to organize a 100+ event that had a staff of 6. We also had a main organizer who was supposed to run the event. Everybody was at least 10 years older then me, but since I was not going to deal with them directly, no problem.
A day before the event, a main organizer came to me and said that I was going to run the event tomorrow. My world collapsed. What was I supposed to do now? omg, omg, omg...
First the event started with a public speech addressing the participants. Of course, I was supposed to deliver that. In the middle of speech I lost my voice. (yay) Then one of the participants rose from his seat and said: "Be quiet everyone, morphy has a gentle, tender voice, so that we can all hear him". Later during the event I was, of course, running all over the place while the staff was idling. Then the main organizer took me aside and told me: "You are going to sit on this chair and whenever I see you not sitting here I am going to take a part of your salary". I needed to learn how to manage and deal with my insecurities very quickly. This is the moment I decided I want to work with people and manage them.

After I graduated I started working as a project manager. I managed big projects with a lot of money, staff (I didn't personally know anything about) and tight schedules involved. I also didn't know a lot about the nature of the project I was supposed to run. But work had to be done. One way how I was dealing with insecurities was putting my boss in cc of every mail I've sent. Soon, my boss stopped reading my mails. The breaking point was thinking to myself "morphy, make a decision, the best one with the data available, and just do it". And I did it. I still ask my boss for input, but now I get responses quickly.

These are just some of the stories from my life and are probably very different from yours. But some ideas can be taken from them. Try making decisions, even small ones and work your way up. Listen the feedback you receive and calibrate your behavior accordingly. There is no failure, only feedback you choose to discard. There are no problems, only opportunities. Try it!

Ok, so what does this has to do with the Game? Do you guys know that moment when you see a girl who you would like to meet and you instantly freeze?
That is, gentlemen approach anxiety (AA). It is a normal, natural process. Every man experience is when approaching girls. Why? It is genetics.
Our brain is hardwired for not lives we are living today but for thousands of years ago when we were all living as homo sapiens in savanna, steppe in tribes. We are only living as urbanized societies for a couple of thousands of years (roughly six), but we lived as hunter-gatherers for nearly 50 000 years. Our genes are specialized for such conditions.
In small tribes there were not a lot of available women (possible mates). Some of the women were either too old or young, some were taken. OK, so when you had narrowed the selection to those couple of available ladies, there were still two life threatening problems:
1. If you had wrong intel, and you started messing with a alpha male's women, you could be killed. He and his friends could literary stone you to death.
2. If you guessed wrong but your delivery was wrong, and you blew your chances you were screwed. Why? Girls like to gossip like they do today. Only problem back then is that whole "attractive/available girl's"' social circle consisted of attractive/available girls. And gossip about your attempt would spread. And you would not have any chances with the rest of the girls. (And you could not move out like you can today).

What were results of 1. and 2.? Those men did not have any offspring to carry their genes. Only those more cautious men (did better intel or worked on their performance more) managed to create the next generation. And that behavior propagated through gene pool (since it had 50 000 years).

What about today? Murder is illegal and highly unlikely. Girls still gossip but unless you are living in a small village, there are always new fish in the sea. There is no real danger by approaching. You simply have to deal with it.

How?

There are couple of techniques but idea is to realize that the irrationality of AA.
1. 3 second rule (by Mystery)
Do your approach before the fear kicks in and you talk yourself out of approaching ("Maybe she has a boyfriends", "She looks busy right now", "She is going to reject me",...).
As soon as you spot someone you like, go. Having prepared something to say before you enter the night club helps.

The scenario (by Roosh)
Find a quiet place and imagine following scenario: So you approach a girl and she starts laughing. She is laughing so hard that she fells. Others notice what you did and start laughing. People whip their cell phones out and start texting, taking photos and videos. Also, there was a TV station crew at the scene and managed to record your approach. And it was a live stream. And it was shown during most popular TV show like news. There is also a TV in the bar where you can see show host laughing his lungs off. Also, there was a live reporting from local stadium where, of course, your approach was seen by thousands of people on big screen. Everybody is laughing and rolling on the floor. They are laughing so hard that they can't help themselves.
OK, do you have this scenario in your head? Yes? OK, now listen very carefully. THIS IS NOT GOING TO HAPPEN! You are probably a smart person (because you are reading this, dough) and you have realized it by now. But you can call this worse case scenario. What is likely to happen is that she will either like you and your delivery (let's call it opener) or she will not and ignore you. So what if she doesn't like it? She will not remember you next day, trust me. You are not as special as you think. Unless you behave as and total idiot and insult her very, very, very directly and stab her or punch her in the face, she will not remember you. You will be "just another guy that approached me that night". (I actually experimented how much can you provoke a girl before she slaps you. Again, unless you act like a jerk directly insulting you, this is not going to happen. Actually, girl will be attracted to you)
Think about it.

Practice makes perfect
Try this exercise: Go to your local shop and ask random strangers questions about some goods there (e.g. "Is this cereal whole grain?", "Do you know where milk is?"). Try making an eye contact as you talk to them. With time, it will be easier and will not be a problem. Next try asking strangers at the street for directions. Again, hold your eye contact while talking. Remember, be polite and thank them for their time.

Approach anxiety will not go away but you can recognize it as normal part of yourself and ignore it.

Good luck and let me know how are you doing.