EAP (English for academic purposes) is about helping students with the English they need to study any subject in an English language program; whether it's in an English speaking country, or not. The students may be studying engineering, economics, education or anything else).
English for academic purposes is one of the main sub-divisions of ESP (English for specific purposes). The other branch is EOP (English for occupational purposes).
Due to the huge increase in students travelling abroad to study at university, and the increase in English language degree programs around the world, there has also been a big increase in the need for training which will help students of any subject, cope with their courses.
Hence English for academic purposes has flourished; or at least it has expanded. Almost every university around the world that accepts students from abroad into its English language degree programs, has an EAP program. These are usually both pre-sessional and in-sessional.
These courses are usually found language centers, or units, within universities. Sometimes the EAP courses are within departments of English, linguistics, education or foreign languages, and these courses are also taught where students are preparing themselves to study abroad in an English speaking country.
English for academic purposes may involve helping students with composition, converting graphs and charts into grammatically correct written English, note taking during lectures, reading academic texts, listening to lectures, or taking part in seminars. It can also require help with building up a subject specific vocabulary. Teaching study skills is usually considered an integral part of EAP.
There are many study skills. These can include: note taking, listening to lectures, asking questions, understanding instructions (both written and spoken), reading efficiently, understanding data, summarizing, research skills, removing distractions, time-management...
Materials designed for native speakers can sometimes be useful. Specific work with particular exams, for example IELTS, is common.
Specialist books on the subject cover this in much more detail, but be warned, they include some of the driest reading in the field of ELT. I've linked (see the right column) to one of the better ones (in my opinion).
Understanding how cultural differences affect students studying in English speaking countries is also important. These can be in classroom interaction (they may not be comfortable asking questions to the teacher, or in expressing opinions which are different from the teacher), styles of writing.
An important part of teaching English for academic purposes is the preliminary and ongoing needs analysis. You need to know what the students need. You also need to know the needs of the educational institution. This is commonly done by means of language testing, self-assessment, observation in class, surveys, interviews, diaries kept by students and case studies.
Most texts on the subject spend a lot of time explaining this in detail, and often the needs analysis is done by the institution itself. Some courses are general English for academic purposes, with students coming from many different subject areas; sometimes the courses are more specialist, with all of the students coming from the same subject area.
For many teachers EAP offers an alternative to teaching general English courses, and it can allow you to teach at a university or college in an English speaking country. English for academic purposes, despite supporting a major industry (that of overseas students studying abroad), has to compete hard for funding against other departments, which are often higher up the pecking order of perceived importance.