It depends on how old is "old". The oldest G3 iMac can run Panther, and the latest, Tiger. They all have the OS X dock.
Purchasing a retail copy of either will be your biggest challenge. Apple no longer sells OS X versions earlier than Snow Leopard. Every time Apple stops selling a retail copy of OS X, aftermarket prices increase dramatically. Search Amazon Marketplace or eBay to locate a copy. It must be the full retail installation version - system-specific discs can be identified by their unique grey color and will not work except on the exact model iMac with which they were shipped.
Not sure what you mean by "external disc". There is no need for an external disc drive if the internal one is working. If it is not working, replace it. Replacement is not difficult if you are sufficiently adept at working on Macs.
Yes, Apple software updates are always free. If you are already running Tiger use Software Update… from the (Apple) menu.
If you are running anything earlier than that, then read: http://support.apple.com/kb/HT5405
To determine what OS X version is installed: > About This Mac
I was wondering, is there a way where I can update it without using an external disc?
If you mean the iMac does not have an internal optical drive capable of reading DVDs, the only option requires another Mac with a DVD-capable drive and FireWire ports. Your iMac G3 will also require FireWire ports. Not all G3 iMacs have Firewire. FW started with the Summer 2000 models with 400mHz and faster processors.
With FireWire, you can use FireWire Target Disk mode to install from a retail OS install DVD in another Mac. If you supplemental info info tells us if you have another Mac with a DVD reader and the FW ports, we can walk you through the process.
If the iMac has a tray-loading drive, I'd forget it. They are very limited not only in the OS max (10.3.9) but also in RAM capability. Starting with the slot-loading iMac G3s, the max RAM increased to 1 GB (2 X 512MB modlules). Tiger likes 1GB RAM.
Understand that pre-Intel Macs are getting harder to use. Even with 10.4.11, your choice of browsers is limited (TenFourFox is the most viable option) and the G3s rudimentary video hardware means web browsing will be choppy at best.
If you are in the USA, you can try calling the Apple Store (1-800-MY-APPLE) for an OS disk. As recently as Jan 20, someone posted here that they were able to buy Tiger by calling. It was not clear whether the disks were replacement system install/restore disks or full retail install, but it's a free call.
When you do "About this Mac" to check teh OS verion, also look at the processor speed and tell us what that says. That can help with recommendations for an upgrade path.
That shows you are running OS9, which does not have a Dock; the Dock came in with OS 10 (OSX). You cannot download a version of OSX. You'l have to find a purchase a disk to install.
We still need to know your processor speed to recommend a path to upgrade. If "About this Mac" does not show your processor speed (can't remember if it shows there in OS9), then there is "Apple System Profiler" in the Apple menu. It's opening page will show processor speed, although you'll likely have to click a number of those pesky little "disclosure arrows" to find and view the proper page section.
Also let us know if you own or have access to a newer Mac. That can be important for upgrading if this iMac does not have a DVD-capable optical drive
Jonathan, you may already have OS X installed, it's just not running in your screenshot. Installing OS X was what caused the folder originally named "Applications" to be renamed "Applications (Mac OS 9)" to distinguish it from the OS X Applications folder which remains to this day.
Go to your Apple menu and choose Control Panel. Open the Control Panel named Startup Disk. Does it show an option to restart using OS X as in the following screenshot?
If "Macintosh HD:System:" appears as an option, select it and click Restart.
Also, before you do that go to the Apple menu and select "About this Computer". Your specific hardware will be listed.