The good news is, 2.4 isn't that old. The bad news is, 2.5 was one of the most significant updates Craft has ever seen. For that reason, you'll want to exercise a little more caution than you typically would need to.
To begin with, backup your database! I can't emphasize this enough... you want to make sure that you have captured a "moment in time" for your site to roll back to, in the unlikely event that it's necessary.
After that, you'll want to perform a manual update. The vast majority of times (99%), an auto-update is a clean and easy way to update your Craft site. In fact, it's one of the things that makes Craft so amazing to begin with! However, upgrading from 2.4 -> 2.5 involves a lot of file changes, so this is one of those rare instances where you'd be wise to upgrade manually.
Lastly, you'll want to update all of your plugins after you update Craft itself. The arrival of 2.5 brought a few breaking changes for some plugins, and several awesome new features for plugins to take advantage of. Besides, it's always best to be running the latest versions of your plugins anyway. :)
In short, set aside 1-2 hours. If you're cautious and follow these tips, you'll almost certainly have a smooth transition. And if something goes horribly wrong, just roll back to your backup, and reach out to the community on the Craft Slack channel.