Hi mandytjie,

Welcome to the forums,
Regardless of my answer, do have a look at: http://manual.b2evolution.net/Upgrade_from_an_older_version

Your personal things are in the folders:
/media/ -> files, images, things you uploaded
/skins/ -> The skins you choose and may have edited
/plugins/ -> the plugins you uploaded.
/conf/ -> some settings, _basic_config.php holds the details for connection to your database.

Copy all the files from the server to your local computer. That is your backup. Make a backup of the database through your hosts cPanel or equivalent.
For the 2.4 version you need to re-upload new versions of nearly all plugins you use.
No skin from 1.10 will work in 2.4, so you need to choose a new skin.

Apart from that the upgrade should run smooth.

The folders in the package are:
- /conf/
- /cron/
- /htsrv/
- /inc/
- /install/
- /locales/
- /media/
- /plugins/
- /rsc/
- /skins/
- /skins_adm/
- /xmlsrv/

If you have subsequent questions please ask!

Good luck

Hya. Thank you very much for your reply. Sorry it took me long to get back to you. The new files are uploading as we speak and I'll let you know if I have any questions.

I do have one. The link you gave me says "Run installation script on server". How do I do that - do I double click one of the php files? If so, which one?

after your done copying the files in your broswer navigate to
http://yoursite.com/yourblogsfolder/install

your site being ur site and ur blog folder being where you just uploaded everything too

and when you type that in it will pop up the script and ask a few basic questions and you'll be on ur way :)

Thank you VERY much for your quick reply! It is all installed. I just need to go about familiarising myself with all the new stuff.