In this introduction I'd like to familiarize people with terms on the defensive line (particularly with DTs) we hear a lot of, but many don't really know the meaning of or don't understand the difference between them. This would be the nose (zero), 3-technique, 4-technique and 5-technique. Too understand what all that means you need to first familiarize yourself the gaps on the O-line, they go from A-D on either side of the Center. The gap between the Center and Guard is the A gap, the B gap is between the Guard and Tackle, the C gap is between the Tackle and Tight End and the D is anything outside of that (although it isn't all that important to this).
A nice little diagram I found online.
Alright so lets start with the Nose Tackle (zero technique). Most people would probably be able to answer if they were asked where a nose tackle played. They play right over the Center (the X in the diagram) and they have a 2-gap responsibility (Both A gaps on either side of the Center) and are there predominantly to stuff the run and free up LBs to make tackles. Rarely will you see a NT penetrate the line when they are well disciplined and true NTs. Their impact is also rarely seen in the boxscore as they tend to accumulate very little in the way of counting stats (tackles, sacks, INTs) but do a lot more than most defenders throughout the course of a game. Generally you would like a Nose to occupy the Center and a Guard on running plays and to push the pocket on passing plays (drive the center straight back and not allow the QB any room to step up). You see NTs most commonly on a 3-4 defense but you can have one on a 4-3 as well.
The 3 and 4 techniques. A 3 technique tackle is lined up between the Guard and OT (the B gap) but shifted inside to the Guard's outside shoulder. 3 technique DTs have 1-gap responsibilities and are asked to penetrate and play the run on the way to the QB in most cases, it really depends on the coaching scheme though. They may be asked to control the gap a little more in obvious run situations. The 3 technique is the most common DT alignment in a 4-3 and is what some of the more notable DTs play in the NFL (Kevin Williams, Albert Haynesworth, Tommie Harris, etc.). The 4 technique is very similar to the 3, they line up in the same gap (B gap) but in the case of a 4 tech guy he'll line up on the inside shoulder of the Offensive Tackle instead of the outside shoulder of the Guard. 4 techniques are very rare and I can't actually think of any team that uses them regularly, they are more athletic pass rushing DTs and the only example I can think of right now was when the 2007 Giants would bring in their 4 DE set on 3rd down and line up Justin Tuck inside, he would play a 4 technique as an extra pass rusher.
The 5 technique is a 3-4 DE, or at least that's the most common place to play them. They line up on the outside shoulder of the OT. Guys like Richard Seymour have made their name as 5 technique guys. They like their interior partner on the 3-4 don't get as much recognition as some other line positions. They compare pretty well to 3 and 4 technique DTs though but tend to be a slight bit lighter and a in a lot of cases a but more athletic. Their job is to free up other pass rushers for the most part but in the process create a pass rush of their own. I'll admit I'm not as familiar with the 5 technique as I am with the 0, 3 and 4 but from 3 to 5 there isn't a massive difference in the type of player.
That covers the 4 most common type of DL position (excluding the 4-3 DE) and there are more than just those techniques. They go from 0 (Nose Tackle) to 9 ( 4-3 Defensive End) but the 1, 2, 6 and 7 are very rarely used and the 8 and 9 have very common names, 8 being the widest alignment on the D-Line anywhere in space outside the TE but inside the Slot Receiver and generally a pass rushing OLB in a 3-4 and 9 being your typical 4-3 DE. Some teams do use the 2 technique at times, like the Lions. Sammie Lee Hill generally plays the 2 technique lining up right over the Guard and maintaining 2-gap control, but it still isn't very common.