Some email clients will allow you to share IMAP4 folders from within the client itself (eg eM Client) or have plugins to allow this (eg Mozilla Thunderbird with the Imap-ACL extension). In that case, you will need to see the documentation for that to set up sharing.
If your email client does not allow you to set up sharing, you can use the VPOP3 Webmail facility to share an IMAP4 folder.
Right-click the folder in the folder list at the left in Webmail, and choose 'Share Folder'. Then, click 'Add Permission' to allow someone else to access the folder. Choose the user you want to share the folder with from the drop-down list in the 'Name' column. Then, choose 'Read', 'Update' or 'Full' from the drop-down list in the 'Preset' column, and press 'Apply & Close'
(If you understand IMAP4 permissions, you can set the exact permissions you want to give rather than using one of the presets)
Once you have shared the folder, the user you have shared the folder with will have permissions to access that folder. However, they may need to refresh the folder list in their email client, and subscribe to the folder. How you do this depends on the email client they are using - e.g. see http://office.microsoft.com/en-gb/outlook-help/subscribe-to-or-unsubscribe-from-an-imap-folder-HP005242608.aspx
The folder will appear as #users/<original username>/<folder name> so that it will not clash with other folders with the same name, either in the user's own folders or folders that other users are sharing with the same user.