Okay It depends on how custom you want to go. Both Twitter Bootstrap and Foundation framework can be utilized.
You can create your own custom theme from scratch or you can create a child theme that uses a base theme.
To create a child theme that uses a base theme.
1. Copy a base theme (any theme you want to start with) into wp-content/themes/
2. Make a copy of the base theme directory you downloaded (and all its content) in the wp-content/themes/ directory changing its name. It is a common practice to add "-child" to the end of the directory name of the base theme used.
3. Go into the new child directory and open the style.css file and change:
Theme Name: <base_theme>
to
Theme Name: <base_theme>-child or whatever you added to to the name of the new directory.
The next line should be Theme URI: leave this the same and add a new line just below this and add the following:
Theme Template: <base_theme>
This tells WordPress that you are using the original theme you downloaded as a parent theme. And it now understands that this is a child theme.
4. While still in the style.css file in the child directory go to the last line of the top comment block and just before the css rule declarations and add:
@import url('../<base_theme>/style.css')
Now WordPress will use the parent version of the style.css file unless the rule is overridden below the @import in the child version.
This is typically how child themes are hooked up.
WordPress always looks for the following files in the all theme directories child or parent for overrides:
index.php
header.php
footer.php
screenshot.png
sidebar.php
style.css
I would also add the function.php file for hooks you need to declare.
5. Applying Bootstrap - Normally the bootstrap directory is copied as a subdirectory into the theme or child theme directory (or both). Then it is hooked up by either adding @import statements to the css and/or paths in the .php files previously mentioned. See this as an example: