The first step is forcing yourself to get behind the wheel and practice, any practice. The hardest part is starting to get over your fear. Driving can be scary, but it’s an important life skill. We’re cheering for you!
I haven’t had the chance to read through this thread so I apologise if I repeat what someone else has said.
The most important thing is to practice practice and practice some more, preferably somewhere quiet and build up your confidence before moving onto busier roads.
As for the ‘not knowing what other people are doing’ thing again that simply requires practice, you’ll quickly acquire a sixth-sense for what other road-users are doing and you’ll quickly notice if something is wrong (like the person on the other lane being slightly out of position and therefore about to swing across in front of you etc)
I grew up in the countryside and I’ve been driving since my feet could reach the pedals (not on public roads!) so I had no problem at all driving around country lanes etc (which is a very different skill than driving on motorways/freeways) but I was extremely nervous about driving around built-up areas and it took me a long time to feel really comfortable doing that.
Good luck! Personally I love driving and its one of my favourite activities.
Buran - Proud Owner of an MR2 Turbo 
27 and I just received my license, so I can feel your pain. My mother was the same way… biting her nails, clutching the armrests, saying in a high-pitched voice “Don’t pull out yet!! There’s a car coming!!” when my foot was clearly on the brake. My advice is to find someone whom isn’t easily exciteable (like your mother) and practice, practice, practice. It really is so freeing not having to rely on anyone else for my transportation. 
Another thing is to become familiar with roads, signs, types of intersections, etc. When you’re on the bus, or in another car, sit near the front and watch where the vehicle is, and start looking for and learning the road signs. You’d be amazed at how many there actually are, and even if there aren’t any painted lines on the road, it’s still really obvious where your direction’s traffic should be. All of these roads and intersections are made to help drivers get through them, not to confuse them, and once you understand the signs and orientations, it will become second nature to them. You know that Burlington has a lot of one-way streets. Well, then, start looking for that one-way arrow, and then you won’t have to worry about turning the wrong way!
Learn the route from your home to wherever you need to go. “To get to the grocery store, I’d have to turn left onto My Street, then go three blocks to the 3-way intersection, watch out, there’s a school there, so slow down, then turn right on Whatever Road and when I see the church on the left, I look for the one-way going left after it and drive until I reach the back entrance to the parking lot, and then I go park”. You can do these things without even getting behind the wheel, and it will help build up your confidence when you have to go somewhere because you already know where to go and therefore won’t go the wrong way/take a wrong turn. One of the people I know who gives the best directions to pretty much anywhere in this city is a 43 year old who never learned to drive (Montreal has great public transit); he just learned the roads and the routes (to avoid looking like some lost country bumpkin, in his words!).
It’s not quite that easy, all the time. Even knowing the roads, it’s still very confusing at times. I used to live on a street that was one-way halfway up, that changed to another street a few blocks down the street from that, and then went two-way, then switched back to one-way another few hundred feet down. The streets were two-lane but only wide enough for about a car and-a-half, and it was pretty harrowing driving around there.
Obviously that’s one specific extreme example, and thankfully I don’t need to go to that area very much, but especially in places where signs aren’t posted or road lines aren’t painted, I get very flustered not knowing quite what to do. Once I have some more road experience, I’ll feel a little better about it.
On the other hand, I’ve gotten very good with directions in the last few years. I couldn’t find my way out of a paper sack in 2005, and now I pretty much can get myself or others anywhere locally that I or they need to go. It’s a pretty big achievement for me.
Also everyone else who responded, thanks for the tips and/or input.
I actually had myself all worked up to give it a shot driving home from work this weekend when there was little traffic, but the roads were all torn-up for construction and my mother (who was giving me a lift) didn’t feel comfortable enough to let me behind the wheel of her car with all the roadblocks up. 
Have you considered getting a program about driving phobia? I googled to find this one. I don’t know anything about it as I just googled for it. But I do know that there are lots of people who have driving phobias and have overcome them. If you can’t afford a program, there are also lots of forums that you can find on the subject where others can tell you what they’ve tried.
Good luck with feeling more comfortable on the road!
Not to hi-jack the thread
This thread reminds me of what I am missing by living in Sydney. Traffic here is bad and I can imagine lot of people being scared to drive in the city. But it is nothing like what I was used to do day in and day out driving in Colombo.
Driving in crazy traffic is sort of an adventure. Driving 25km taking 1.5 hours after work makes you feel like a winner when you come home in the night.
I miss driving in Sri Lanka.