Available options to implement a knowledge base or FAQ repository?
Ticketing system

Implement a ticketing system, using the Support module. Popular/great module, to the extend that you can live/agree with the design / assumptions / etc of this module. Definitely worth considering to "get started". Here is a list of features (from its project page):


  
  Ticketing activity is illustrated with colorful charts (depends on the Chart API module).
  Tickets can be assigned to users (and users can view all tickets assigned to them).
  Tickets support states (new, active, pending, closed, etc) and priorities (low, normal, high, critical, etc).
  Configurable email notifications for new and updated tickets.
  Email integration allows tickets to be created and updated via email, with support for attachments. New users can be automatically created. Ticket properties can be updated via email (using included support_mailcmd module).
  Highly configurable client and user ticket overviews, highlighting tickets that haven't been updated for a long time.
  Fully integrated with Drupal's search functionality, users can only search for tickets they have access to.
  Supports an unlimited number of clients, each with their own configuration and access permissions.
  Tickets are nodes, ticket updates are comments.
  


Wiki system

Implement a wiki system, using modules such as these ones (excerpts are from their project pages):


Wikitools:


  ... provides some settings to get a more wiki-like behavior. It aims to be lightweight; all features are optional, and it provides no database tables of its own.
  
  Some of the features of this module are:
  
  
  Node Creation: Let users create new nodes when they type in a node name which does not exist.
  Node Search: Let users search for nodes when they type in a node name which does not exist.
  Automatic Redirect: If a title of a moved page is entered, redirect automatically.
  Unique Titles: Enforce that titles are unique over all wiki node types.
  Move Protection: Disallow change of node titles for users without administer nodes permission.
  Underscore as Space: Treat underscores as spaces when doing a node-lookup by title.
  Dash as Space: Treat dashes as spaces when doing a node-lookup by title.
  Custom wiki 404 pages: pick and choose from links to create, links to search, and an inline node add form.
  
  
  The module can be used in conjunction with the flexifilter module (of course), the freelinking module by hijacking freelinking links, or together with the pearwiki filter module for various wiki formats.

Freelinking:


  ... implements a filter framework for easier creation of HTML links to other pages on the site or to external sites.
  
  The framework uses a wiki style format such as [[indicator:target]] as markup to identify links.



The video about Setting Up a Wiki in Drupal 7 contains an interesting introduction to the modules mentioned above (and some other modules you might also want to consider for this purpose).

There is also the Wiki installation profile (either just use that profile, are review it to get inspiration about possibilities). Excerpt from its project page:


  ... will set up Drupal with the following settings:
  
  
  Moderator role which can revert / delete pages.
  Revisions for pages.
  Freelinking - easier creation of HTML links to new or existing pages.
  Edit a section of a page (based on header).
  Mediawiki input format.
  Categorization via free tagging vocabulary.
  Views: All pages / All categories / All Images.
  Recent changes.
  


Questions &amp; Answer site

Implement a questions &amp; answers site (similar to "Drupal Answers" here ...), using the Answers module (Disclosure: I'm a co-maintainer of it), for which a Demo site is available.

To experience it yourself, here are the steps to try it out:


Head over to this sandbox site.
Just accept the defaults to create a sandbox demo site (hit the create sandbox button, and wait for the process to complete).
Login to the site (using the suggested defaults).
Create at least 1 question using either the "Add content" menu link and then selecting "Question", or just enter relative path /node/add/question. And complete the title and body of the question.
After you save the question, you'll see the question that's created (in view mode). And below the question, you should see "No answers yet." (since you just completed posting the question). And then there is the "Your Answer" form right below that. That is the form you can use to post an answer to the question.
If you then use that (answer) form to post your answer, and also save that, the (first) answer is shown below the question, and below that answer there is now the "Your Answer" form again (to allow for posting an additional answer).
Use the Questions tab (or enter relative path /questions, to get a list (a tabular display) of all existing questions so far (there should be at least one if you completed the previous step).


Note: you may also want to enable the Answers Theme (sub-module of Answers, new as of 7.x-4.x). After you do, return to the question you created before, and see how the look-and-feel of both the question and related answer(s) below it changed ... Here is a sample screenprint of it:



Groups of users

If your target audience consists of multiple groups of users, then you might want to use the Organic Groups module also.

A great resource for learning about Organic Groups is the (free) video training about Learn Organic groups, a set of 14 videos.

As an alternative you may want to consider the Group module, which only exists as of D7, but already has a pretty stable D8 version also.

Roll your own cookies

After you become more familiar/experienced with Drupal, you could just build your own custom solution. With only site building techniques (using contributed modules), you could probably get pretty far. E.g. using modules such as the Frequently Asked Questions module.

However, I you want more flexibility and (way) more facilities that can be perfectly tuned to your specific needs, then you should consider using modules such as:


Views (Video tutorials: Learn Views).
Rules (Video tutorials: Learn Rules).
Flag (Video tutorials: Learn Flag).
Message (More docu in its Community Documentation).