Hi - depends on the bike. Most need front wheel installed, attach bars, insert saddle/post, inflate tires and check shifting adjustments. Attach pedals. Tighten / check overall bike parts even those that arrived installed - check out this assembly page:
There is a MTB video and a cruiser assembly video along with other helpful info and more videos:)
http://www.bikesdirect.com/instructionhelp.htm

Above answer is an accurate answer. Here is an answer from a customer of BD to give you more perspective. In short, I really like these guys. I havne’t had any trouble asking them questions over the years, and I have been really happy. I always recommend people buy from them. But as far as assembly I see this as a great concern people have when ordering these bikes so I’ll try to be detained to help others.
I have purchased 2 bikes over the years from BD. The expectations were mostly clear, but here is what you have to do listed out with some details and commentary. Youtube is your friend  just about anyone can do these tasks nothing is “hard”. My only concern is people that tend to shortcut tasks and don’t respect that you are putting together a vehicle that could be dangerous if not assembled properly. I am a software engineer by trade so we tend to be a pretty detail oriented bunch if this isn’t you I’d take it to a bike show or find someone who is and buy them dinner. With these guys you get a great bike for a very reasonable price (the best I am aware of). The frames are really good. I have two of their titanium frames, and have seen their Al. About me I have built numerous bikes, and do auto work and generally do a lot of work with tools; even a novice will be ok as long as you take your time. I would watch some youtube video's posted on each of the following tasks to make sure you are comfortable doing what I suggest. Note most of these “tasks” once you own a bike you’ll have/should to do anyway on a periodic basis so in my mind it minimizes this as a tax.
Note my purchases One road and cross + disk bike Titanium.
Here are the tasks you “may” have to do depending on the bike.
Prerequisites Patience no rush 
Minimum: You will need grease (as a general rule metal on metal threads need grease), and tools (hex metric and star style disk brake)
Class 1: You need to know this stuff anyway
1.) You have to put on the bike wheels and inflate
2.) seat post and adjust seat add/tighten petals
3.) shifting adjustment. Normally they come close but not perfect, and on a lower end bike they will be more finicky. This is really easy to do bike shops always make it sound like a big deal, but you’ll want to know how to do it anyway since any new bike will have cable stretch and it is a pain to bring it into a show every time you need to tweak the gears.
4.) I would expect to spend some time fitting the bike. Little things like centimeters can make all the difference in the world to your comfort. Generally, this entails moving the seat around and the handle bars up and down. It may include adding additional accessories such as stem raisers, shorter stems etc if you feel you want to be more upright for example etc. If you were in ball park in sizing the bike though this will be just moving stuff around. But honestly even just getting a seat in the perfect position can take 10 minutes with all the getting on and off and stuff.
5.) I would check every bolt on the bike especially around the headset, brakes, and crank. Verify they are tightened properly, and do this periodically. In my experience they come tighten properly but I see no certificate on there that says they have been tested and it is a safety issue.
More specialized tasks.
1.)Handle bar/headset attachment. If you get a carbon fork, you really should invest in a basic torque wrench (newton meters) you can get good ones on amazon for about 20 they are totally worth it *I use it on the previous task). This is a simple task if you know the steps but you need to get the steps for the bike you are purchasing. Some screws need to be tighten before others etc, and the must be tighten with in the tolerance. You should do this periodically with any bike you own ( yearly when you do your maintenance).
2.) brake adjustment. Note with disk brakes this isn’t entirely trivial it is with traditional brakes. With disk there are very low tolerance and especially lower end can be a little tricky when it is your first time. In my experience if you get a disk and the rotor isn’t trued well this can take some time to get right. This is really the only tasks that out of the box can require a little practice similar to wheel truing albeit not that difficult. There are great youtube videos online though on the subject though. It if is your first time probably e2e it is 30 minutes to get the instructions and make the adjustments.
3.) The head set and crank on my bikes from them have come greased so you don’ t need to do anything, but you may want to check. I usually add a little more grease because I take it apart and inspect it, and like to make sure everything is tight so dirt doesn’t seep into the crank. I live in seattle and mud and sand is always a problem so I am pretty anal about getting all that sealed up and lubed. This is not really necessary but if you want to geek out I’d go ahead and do it.

Test
Also when you test a bike wear a helmet even for simple stuff weird things can happen and give everything a good test before you jump on. Pull the hand around, flex the brakes turn the bike upside down an verify the shifting pull on the wheels. Push down on the seat and pull up twist. Do these things before you jump on and test. These are all things a bike shop would do before they hand a new bike over to a customer and you should do it too. Also a bike with disk brakes needs some burn in just like a car, and lesser so with regular brake. But initially disk breaks are actually really weak until you do this. So do it in your drive way or sidewalk but stay off the road until you are confident and it tightens up.

My estimation if you don’t know what you are doing, and have minimal experience with tools this is a 2-3 hour job depending on the bike. If you know what you are doing, and have a more complex setup it can be done in about 30 minutes. My last build took me an hour because the brakes took a while and I had to recut the housing and run new cable since I was adding a stem raiser, and there wasn’t enough extra cable. I also took everything a part and put it back together manually.

There are also excellent books on bike building. I’d stick with youtube though it is easy to search for you specific parts etc.