Several of these other answers are very good. I'll try to fill in some things they haven't mentioned.
EDI is a set of standards, the most common of which are:
- ANSI X12 (popular in the states)
- EDIFACT (popular in Europe)
Sounds like you're looking at X12 version 4010. That's the most widely used (in my experience, anyway) version. There are lots and lots of different versions.
The file, or properly "interchange," is made up of Segments and Elements (and sometimes subelements). Each segment begins with a two- or three-word identifier (ISA, GS, ST, N1, REF).
The structure for all documents begins and ends with an envelope. The envelope is usually made up of the ISA segment and the GS segments. There can be more than one GS segment per file, but there should only be one ISA segment per file (note the should, not everyone plays by the rules).
The ISA is a special segment. Whereas all the other segments are delimited, and therefore can be of varying lenghts, the ISA segment is of fixed width. This is because it tells you how to read the rest of the file.
Start with the last three characters of the ISA segment. Those will tell you the element delimiter, the sub-element delimiter, and the segment delimiter. Here's an example ISA line.
ISA:00: :00: :01:1515151515 :01:5151515151 :041201:1217:U:00403:000032123:0:P:*~
In this case, the ":" is the element delimiter, "*" is a subelement delimiter, and "~" the segment delimiter. It's much easier if you're just trying to look at a file to put linebreaks after each segment delimiter (~).
The ISA also tells you who the document is from and to, what the version is (00403, which is also known as 4030), and the interchange control number (0000321233). The other stuff is probably not important to you at this stage.
This document is from sender "01:1515151515" and to receiver "01:5151515151". So what's with the "01:"? Well, this introduces an important concept in EDI, the qualifier. Several elements have qualifiers, which tell you what type of data the next element is. In this case, the 01 is supposed to be a Dunn and Bradstreet number. Other qualifiers for the ISA05 and ISA07 elements are 12 for phone number, and ZZ for "user defined". You'll find the concept of qualifiers all over EDI segments. A decent rule of thumb is that if it's two characters, it's a qualifier. In order to know what all the qualifiers mean, you'll need a standards guide (either in hard copy from the EDI standards body, or in some software).
The next line is the GS. This is a functional group (a way to group like documents together within an interchange.) For instance, you can have several purchase orders, and several functional acknowledgements within an ISA. These should be placed in separate functional groups (GS segments). You can figure out what type of documents are in a GS segment by looking at the first GS01 element.
GS:PO:9988776655:1122334455:20041201:1217:128:X:004030
Besides the document type, you can see the from (9988776655) and to (1122334455) again. This time they're using different identifiers, which is legal, because you may be receiving an interchange on behalf of someone else (if you're an intermediary, for instance). You can also see the version number again, this time with the trailing "0" (0004030). Use significant digits logic to strip off the leading zeros. Why is there an extra zero here and not in the ISA? I don't know. Lastly this GS segment also has it's own identifier, 128.
That's it for the beginning of the envelope. After that there will be a loop of documents beginning with ST. In this case they'd all be POs, which have a code (850), so the line would start with ST:850:blablabla
The envelope stuff ends with a GE segment which references the GS identifier (128) so you know which segment is being closed. Then comes an IEA which similarly closes out the ISA.
GE:1:128~
IEA:1:000032123~
That's an overview of the structure and how to read it. To understand it you'll need a reference book or software so you understand the codes, lots and lots of time, and lots and lots of practice. Good luck, and post again if you have more specific questions.