While it's not exactly easy these days to get tickets, with how popular the show is, it can be done. And there's no secret to it either - I got tickets the very first time I tried, with no other knowledge than the instructions laid out on tvtickets.com.
Getting the tickets
If you randomly take a look at the show page for Big Bang Theory, chances are you won't find anything other than a blank space under "Available Show Dates." If you keep checking back randomly, you might get lucky, and be there at a time when they've released another small batch of tickets for an upcoming taping. These might go up weeks before a taping, or as soon as the day before - but there's no pattern (at least that I've noticed), and no guarantee.
What you really want to do is get the tickets as soon as they go up, which is at a scheduled date and time. From Big Bang Theory's page, you can view their future show dates, which typically lists dates about three months in advance. However, the tickets aren't actually released until 30 days prior to the taping.
Because Big Bang Theory tapes on Tuesdays, the 30 day mark falls on Sundays. But the site doesn't update on Sundays, so the ticket release is pushed back one day until Monday mornings.
Once you've figured out the date the tickets will be released on, you want to plan on being up early that morning to check the website. The tvtickets website says that "the show schedule automatically updates around 8:30am (M-F Los Angeles time) to display shows scheduled for the next 30 days." But sometimes the tickets are released closer to 8:00am, and sometimes they're not released until 9:30am or later - so be ready for lots of refreshing.
Big Bang Theory's main page will update under "Available Show Dates" when the tickets go up, but you can also directly refresh the ticket order page and watch for Big Bang Theory to be available in the drop-down list.
Remember that you must be at least 18 to be admitted to a taping for Big Bang Theory. (They make exceptions for VIPs, but if you're reading this guide, chances are you're not a VIP.) And if you're getting multiple tickets, you must fill out the form for each person individually.
The first tickets to go up will be guaranteed tickets - if you're lucky to get one of these, congratulations! As long as you check-in on the taping date before 5:00pm, you have a guaranteed spot in the audience waiting for you.
After the guaranteed tickets are gone (which normally takes no more than 5 - 10 minutes), the standby tickets are released. Standby tickets are clearly marked by the word "STANDBY" in all caps on your ticket after the show name. With a standby ticket, you are not guaranteed entry. If there are any seats left on taping day after the VIPs and guaranteed ticket holders have been admitted, they will let in people from the standby line.
Be sure to print your ticket! You won't be emailed any confirmation. If for some reason you are unable to print, you can still check in with just your ID (they'll find your name on their list), but it's definitely easier to have the physical ticket in hand.
Now that you have your ticket, let's jump ahead to the taping day itself!
When to get there
Your ticket will suggest that you arrive to check in "no less than 90 minutes prior to the scheduled show time." The taping starts at 6:30pm. But if you show up at 5:00 with a standby ticket, you have an incredibly slim chance of getting in.
So how early should you get there? The parking garage where you'll be parking typically won't let in Big Bang Theory audience members until 2:00, but it's not uncommon for the line itself to by starting by 12:00 or 1:00. These people have either been dropped off, or have found parking elsewhere and walked to the line location.
It's impossible to give a "safe" time to arrive by - sometimes lots of people arrive really early, sometimes the line stays smaller until closer to 3:00. Plus regardless of how early you get in line, you still don't know how many seats will be left over in the end for the standby line. Just remember, the earlier, the better.
(And if you've got a guaranteed ticket - remember, as long as you're there before 5:00, you're good. But if you get there after that, you'll be placed in the end of the standby line.)
You won't be actually checked in until 4:30, and it's at that point that they'll number the tickets of everyone in line.
What to bring
Most importantly, make sure you have an ID! Security will check it to make sure you're at least 18, and you won't get into the studio without one.
I recommend eating a big lunch, and/or bringing snacks for the long wait. There are vending machines in the waiting area, but you might want something else. And although you will get a slice of (cold) pizza during the taping, if you've already been in line a long time and haven't eaten since noon... It's not enough.
Do not bring cameras or cell phones. While in line, you will be told, repeatedly, to leave them in your car. And you will go through two metal detectors, and a thorough bag search, before being led to your seats. If you have one, they will most likely find it.
If they find it at the soundstage, they will hold it along with your ID until the taping is finished, at which point you can pick it up on the way out. But to avoid the hassle, if possible, just leave them in your car.
Once the taping is over, the cast might stick around to sign autographs. Some sign more often than others, but I have never see Jim or Mayim sign. On the other hand, Kunal signs almost every week (and is extremely sweet). They won't always have their own pen, so it's smart to have one handy. Most people ask the cast to sign the small program that is given out to the audience members. You used to be able to bring DVDs, magazines, etc., to ask them to sign, but starting in season 5 that's no longer allowed. (If security finds any such items when you get to the sound stage, they'll hold them until after the taping is over.)