I had to overcome this many times throughout life too. I'm naturally introverted and shy, but have had to get past it again and again and again. Finally in my 40's, I'm much more fearless and secure. They say we "come into ourselves" as we age, and for me it's true. I guess forcing it so many times finally made me realize it's not scary. If I had the power and security in my 20s that I do now, my life would have taken a much bolder course-but hey, never too late I guess.
Some of the most valuable pieces of advice I got about it may sound harsh, but I find a lot of truth in them. One teacher told me, "shyness is selfishness". Of course that is outrageous, many people are naturally shy and they are not selfish, but the point is, when you don't reach out, you don't give others the opportunity to feel good, and you don't show your interest in them. Think of how wonderful you feel when someone nice approaches you, smiles, and asks you how you're doing and who you are. Then an interesting talk ensues, you've made a connection with another human, and you walk away feeling great. It's not fair for you to never do that for people. And another great saying is, "It's not about you". Often, we're so worried about how others will perceive us, we want to hide. But no one cares. Everyone is thinking about themselves, and noticing the people who are either really outgoing and showy, or really mean, or even just nice and interactive. They're literally not noticing the people slipping quietly by in the background, and it's no one else's job to come scout you out. If you want friends, you have to make a move. You don't have to perform or be impressive, just smile and make eye contact on the way through the office each trip to the water cooler. Use the line, "hi, I'm ____who are you?" with a smile. It's that simple. Strike up a little chit chat. Don't overdo it. But you can feel awkward and shut out for MONTHS in a new job OR you can start asking people questions (easy to do when you're new), ask about themselves, and show you are open and nice. Don't be fearful that suddenly you'll have to do all kinds of after work stuff or anything, just be friendly at work. Participate. It's hard, but you can do it.
Make a hit list of the people in your office you WILL initiate a conversation with. Cross off two per week. Approach, ask question, whatever. And walk around slowly and confidently making eye contact, smile, and say "hi" when you pass. Don't race around with your head down doing the "busy" walk all the time. If there's a way to join people at lunch, do it.