Initial Steps
The first steps to start in the technical realm is to understand at a high level what are the different custom objects possible. Commonly termed as FRICE, RICEF or RIEF - these abbreviations denote all the possible kinds of custom development common in any SAP project.
F = Forms
R = Reports
I = Interface
C = Conversion
E = Enhancements
Depending on the business requirement and the nature of the module each custom development can be classified as one of these. For example an custom development in the inbound CIF exit for populating APO-specific product master field is an Enhancement. However these are not all the technical objects which are either Function Modules, BAPIs, User-exits, BADIs, Tables, Forms, Module Pools etc. etc. Don't worry as a functional consultant you need not know all the details but just an overview is sufficient enough to get started towards custom development.
This is as far as the technical objects. The other important aspect of any custom development is documentation. Most common document is a Functional Specification (FS) followed by a Technical Specification (TS), Component Specification, Unit Test Plan (UTP), Code Review and so on. As a functional consultant the most common documents you will use / work with is the FS and UTP. The FS outlines the business requirement translated into the functional design of the custom development required. The UTP on the other hand will list out the steps and points to be tested both positive and negative to ensure the custom development serves the business requirement.
Now coming back to the most important question we have in mind - how do I come up with the design of the custom development and then identify the custom objects required. Well this comes a) with experience and b) working closely with your ABAP team unless of course you moved from a Technical Consultant to a Functional Consultant 
As a functional consultant your first place to look for custom objects starts in SPRO - Customizing. This is where under Enhancements or BADIs you will see the list of Userexits and BADIs possible for each application area. The other way is SE18 or SMOD for BADI Definitions and Classical User Exits respectively.
The next one would be transaction BAPI under which by application you will find the BAPIs (kind of function modules) that can Get, Update, Delete and Save different kinds of Master and Transaction Data.
Beyond this it becomes fairly technical - basically you search for function modules using SE37 or reports using SE38.
Of course you can use SE80 (Object Navigator) to search for any kind of technical objects. Actually it helps to narrow down the search if you know the relevant Function Group or Package.
How to find the relevant starting point? Well easiest is do a F1 on the standard delivered object and then hit the Technical Information button (4th from left).
So much for the first steps.