There are currently several thousand extensions listed on the Joomla! Extensions Directory, also known as the JED (http://extensions.joomla.org), so it would be very difficult, if not impossible, for one person to be familiar with all of them. As a result, we will need to take our time finding just the right extensions.
Luckily, the JED is divided into categories where we can view all the extensions related to that category or topic, and it can be searched along with the Internet in general, for extensions that we want. Alternatively, we can ask other people we know who might be more knowledgeable than ourselves.
The best way to use the JED search is via the advanced search feature, which can be found at the top of the page and to the right of the search box as shown:

When searching for extensions though, I actually recommend using Google over using the built-in search on the JED if possible, as at the time of writing, the search is not as useful as it could be and tends to bring back excess results. Google searches, when limited to the JED domain, tend to bring back narrower, more accurate results.
To limit a Google search to a specific web site, first click the Advanced Search link on the right-hand side of the search box, as shown:

On the next page, in the Need more tools? section, enter extensions.joomla.org into the Search within a site or domain parameter as shown:

Choosing extensions from our goals
Once we have our goals worked out, and an understanding of how to search for extensions, it is time to actually start choosing the extensions we will use.
An important thing to consider as we start this process is the difference between Core and Third Party Developer (3PD) extensions.
Core extensions, are those that come with Joomla! by default, such as the content component, web links component, and contacts component. These extensions are developed and maintained by the Joomla! project team itself and generally get updated (if needed) automatically with Joomla! releases. They are mostly broadly aimed extensions that most people will use on a site, such as user management, content management, contacting the site, displaying links to other sites, and so on.
3PD extensions, on the other hand, are those made by people working separately from the Joomla! team. These extensions will generally be updated when the developer makes changes or fixes and are not reliant on Joomla! releases. 3PD extensions can augment or extend the core Joomla! Extensions by adding new features or they may introduce completely new functions and extensions, such as galleries, social networking, and so on.
When choosing extensions to meet our goals, it is often best to start with the Core extensions before looking at 3PD extensions. The reason I recommend this is because Core extensions are often more closely integrated with Joomla!, and are less likely to be affected negatively when a new version of Joomla! is released. 3PD extensions are developed separately and so a new Joomla! release may cause problems that a previous one didn't.
So, firstly we want to compare our goals to the Core extensions and see if any of them meet our needs.
Once we have compared all the core components to our goals, we can start searching for 3PD extensions that meet our goals. Remember to search for ones that best fit our goals, and not just grab extensions we like, then make goals up to suit them, otherwise we will definitely end up with a Frankensite.
The first place to start would be to check the relevant categories on the JED, even before using the JED search or Google. Then, if we can't find any extensions that meet our goals, the next step would be to use the JED search or Google.
A couple of other places to look are the various featured extension pages on the JED, such as Most Favoured, Editors' Pick, Popular Extensions, Top Rated, and Most Reviewed because there is a good chance that other people have attempted something similar to what we are trying to do, so we may find some good extensions that match our goals there.
Let's see the process in action with our sample site.













