Where am I?
Your first attempt at playing a seven stringer can be confusing. When I bought my first seven string (a Gretsch) I thought "no problem." It looked familiar. Yes, there was the extra string (A) on the bottom side. So? I figured I could play the six strings as usual and use the seventh now and then until I got used to it. Wrong. Simply understanding that there was a seventh string was not the same as reconfiguring my visual gestalt. My mind kept flip-flopping from thinking "the extra seventh string is on the bottom" to a denial of "no, the lowest string is E, as it has been for years, and the seventh string is...jeesh, where is it!" Years of playing six strings interfered with any simple passage into the seventh string world. Not totally realizing this, the same day I bought my guitar I took it to a Broadway musical I was playing in. Oh my. On and off pit musicians were staring at me like I had lost my bearings. Indeed I had. Your experience may differ, and I certainly hope it does.
Grappling with the beast
The easiest way of approaching the seven string guitar is to consider it a six string guitar with an extra octave lower A on the bass side. That is what it is. You can play the same notes you would play on the fifth string on the seventh string. It's a real rush when you first try it. Instant depth an octave lower! If skipping the fifth string in favor of the seventh is done too frequently in a piece, however, it may start sounding like there is a "hole" in the range where the fifth string notes lie.
Unwrap that thumb
A physical consideration of playing the seven string beast is that you will have to put your left hand thumb under the neck just as your first guitar teacher said you should. The neck is just too wide to be casual about the position. If you play classical guitar, you are already familiar with stretching further. If your hand position is closer to Richie Haven, you may have a problem.
Won't you be my neighbor?
You can quickly spot your new neighbors on the seventh string. What do you see? Notes so low that you may have to to count the ledger lines to figure out what they are. I bet you haven't done that since your first guitar lesson. Relax. Of course you should know them, but you will never have seven string music put in front of you. In the music books and sheet music industry, it just doesn't exist. Maybe you would like to write some? Maybe not. Notice also the seven string TAB. You won't find that at your corner music store either.
The six open strings plus the seven lower notes on the seventh string
Six string harmonized scale
As mentioned above, the primary advantage of the seven stringer is the depth of the low A. Here is a standard harmonized major scale playable on the six string guitar. The fifth of the chord is omitted.
Seven string harmonized scale using the low A string
In short, the possibility of a piano-like spread of sound distinguishes the seven string guitar.
Real life four-bar introduction using six strings
This intro is arranged so that there are low bass notes whenever possible.
Same introduction using lowest possible bass notes
The above example shows the large amount of ledger lines needed. It doesn't make for fun reading and takes up a lot of space. If I need to write a seven string arrangement for a student, I use the standard six string notes and insert a "7" next to the note that is supposed to be an octave lower.
The only difference between chord sets using the seven string guitar is that you now have an extra chord configuration to play with. All three of the same standard Dmaj7 chord below have the same voicing (disregarding octave displacement). The first one played at the second position includes the seventh string.