(A) a needs analysis for the students concerned.
The Council of Europe's Waystage and Threshold Syllabus Specifications by J.A. Van Ek and J.L.M. Trim were the first really useful attempt to link language patterns or structures to functions. I found the 1980 edition a more useful working document than the 1990 one. More recent revisions have involved very long documents. An easier checklist could prove more useful given time constraints in most schools.
(B) A description of the national and institutional situation for which the syllabus is being prepared.
For such a description, see:
Readings in School-based Curriculum Development  - Malcolm Skilbeck's Situational Model of Curriculum Development
Roger Bower's model for Project Management and Performance pages 99-120 in ELT Documents 116 Projects for the Third World (originally published by Pergamon in association with The British Council) - a very interesting read by someone who has really done the job!
(C) Operational objectives for each skill taught at each level.
There is a close connection between syllabus design and test design. The link can be seen clearly by looking at an examination syllabus (such as the University of Cambridge's First Certificate in English). This ultimately leads to a test. The test reflects the syllabus.
One way of viewing a syllabus is through the behaviours which the educating bodies are trying to teach learners to perform. These can be specified in the form of operational objectives, which contain formal categories such as quality and speed of performance. For this kind of description, see:
ESU Framework by Brendan J. Carroll and Richard West . This contains the English Speaking Union's performance scales (descriptions for all the different 'bands' or levels) related both to general English and the skills of listening, speaking, reading and writing.
In classes of beginners and elementary level students, care needs to be taken to teach grammatical structures in an order which makes it possible for learners to move gradually from the familiar to the unfamiliar. It should still be possible to use functional vocabulary and settings, though focus on syntax at these lower levels is inevitable.
Most TEFL Certificate Courses should therefore still be setting questions like this for trainee teachers to answer:
EXAM TITLE: In what order would you teach the stuctures listed below to a class of adult beginners, and why?
Is it at all possible to grade a language course purely on notional / functional criteria?
How far do any two of the language courses you know which are based on structural grading meet notional / functional demands?
Above are the stuctures that you graded before when asked to specify the running order of a syllabus based on structural difficulty alone.
What functions can you ascribe to them and in what order would you teach them in a functionally oriented course?
1. To be + noun - Introductions; asking personal information
2. Possessives - possession; your name/his name
3. Prepositions of place - stating position/destination
4. Present Continuous - Describing actions; stating destinations / future reference
5. Pronoun objects - ordering/offering/naming
6. Can - possibility/request/ability knowledge.
7. Present Simple + ing - Getting/giving information; jobs; habits; likes/dislikes
8. Do you Qs - Asking for information: job/hobbies/likes
9. Present Simple (neg) - dislikes
0. Q-word + do you - habits/routines/timetables
11. Adj/adv - describe manner
12. Comparison of adverbs - comparison
13. Have/have got - possession/description
14. Present Perfect - interest in past events / state experiences.
[From a Stockholm 1981 TEFL Training Course given by David Jones]
1 Notional Syllabuses (1976) - A Taxonomy and Its Relevance to Foreign Language Curriculum Development (ELT) by D. A. Wilkins. This covers the early attempts of functional syllabuses ('analytic' as opposed to 'synthetic') dating from the mid 1970s, though Speech Act Theory and phrase books for tourists already existed! D.A. Wilkin's seminal work nevertheless influenced the direction of language coursebook design.
2. Actos De Habla de la Lengua Espanola by Jesus Fernandez Cinto . This illustrates a functional approach to language syllabus design in Spanish. It's always good to review syllabus design in a language which is not your own. This work is superior to a situationally based phrase book since it plots the functions needed for 'good survival' Spanish. It also shows that Speech Act Theory, which originated in the USA, has long been international.
3. Approaches and Methods in Language Teaching by Richards, Jack C. and Theodore S. Rodgers [16/06/2014] Cambridge Language Teaching Library. Although not limited to 'functional syllabuses and approaches', this provides an up-to-date survey.
4. Speech Acts: An Essay in the Philosophy of Language by John Searle 
The heart of this work is contained within a few inspired pages in the middle. If you are interested in the developments in linguistic description and semantics, which were further refined by D. A. Wilkins and Wilga Rivers in their more communicative categories for language course design, then Searle's concise taxonomy is well worth looking at.
5. How To Do Things With Words by J. L Austin [2nd Ed. 1975] also predates Wilkin's reseach.
6. Teaching Language as Communication  by Henry Widdowson. This is another of the seminal works leading to greater emphasis on 'a functional thread' in language syllabus design. It presents concepts, such as the difference between "signification" and "value", which played a key part in changing the direction of language syllabus design from the late 1970s onwards.