This topic has been discussed a lot around here...I'll give you a brief summary:
Clock speed = bus speed x clock multiplier
PIII 450Mhz = 100Mhz x 4.5
Celeron 400Mhz = 66Mhz x 6
etc...
All Intel chips have fixed clock multipliers, which means that the only way to overclock is to adjust the bus frequency.
Consider your PIII 450Mhz...
100 x 4.5 = 450Mhz
112 x 4.5 = 500Mhz
133 x 4.5 = 600Mhz
Problems with adjusting bus speed: 1) your motherboard must support the adjustment. Many boards will *always* use the CPU defualt. 2) Your motherboard must support small enough adjustments, some only do 66/100/133 which is not handy for overclocking 3) Adjusting system bus speed will also effect the PCI and AGP busses.
In regards to #3. PCI and AGP run at some multiple of the system bus speed, and they *always* want to run at 33 and 66Mhz respectively. The selectable multipliers will depend on the chipset on your motherboard. Typical 440BX PCI multipliers are 1/4, 1/3 and 1/2 and typical 440BX AGP multipliers are 2/3 and 1/1. I mention the BX multipliers because you probably have a BX or similar motherboard. Another note: PCI and AGP busses must always run at their minimum speed or better. Let's do numbers:
66Mhz system bus * 1/2 PCI Mult = 33Mhz PCI bus (good)
66Mhz system bus * 1/3 PCI Mult = 22Mhz PCI (no good)
100Mhz system bus * 1/3 PCI Mult = 33Mhz PCI bus (good)
112Mhz system bus * 1/3 PCI Mult = 37Mhz PCI bus (ok but risky)
112Mhz system bus * 1/2 PCI Mult = 56Mhz PCI bus (no way)
100Mhz system bus * 2/3 AGP Mult = 66Mhz AGP bus (yay!)
112Mhz system bus * 2/3 AGP Mult = 75Mhz AGP bus (ok, risky)
112Mhz system bus * 1/1 AGP Mult = 112Mhz AGP bus (NO WAY)
Ok, so obviously it's best to run at a standard bus frequency of 66 or 100Mhz. Jumping up to 112Mhz on your PIII, for instance, means running PCI at 37Mhz and AGP at 75Mhz. What are the risks here? Everything on your PCI and AGP busses is now being overclocked, which can lead to failure, data corruption (remember, your HD controller is on there too), and so on. However, most devices can run a bit above their minimum rating without too much trouble. In the past I've run AGP at 83Mhz and PCI at 42Mhz without problems.
What about 133Mhz, it's standard, right? While you can select a PCI multiplier of 1/4 to run PCI at 33Mhz, there is no appropriate AGP multiplier on BX-grade chipsets so you're going to overclock your AGP card no matter what.
What about AMD? Durons and Athlons can be overclocked by adjusting the clock multiplier, which means that you don't have to worry about bus frequencies. It requires scratching the processor with a pencil a bit, but it works.
What can you expect to gain from overclocking? On the average you should expect a 10-20% improvement in clock speed. Your 450 might be able to jump to 500-550Mhz without too much trouble, but you will be running out of spec PCI and AGP. AT BEST you'll be able to jump up to the next standard bus speed. On your PIII 450 that means 4.5 * 133Mhz = 600Mhz.
More to think about: heat! You might need a better heatsink/fan, and you'll want to mount it with good thermal transfer compound. Investing in another box fan might be a good idea too.
More to think about: memory! To overclock your PIII you'll want at least PC133.
Is it worth it? On a PIII processor no, not really. I would only recommend it in certain circumstances (e.g. overclocking old Celerons was awesome). With an AMD processor I'd absolutely recommend it...you've got nothing to lose!
I suggest you see what your motherboard can handle, and then buy a Celeron II 800Mhz processor or better. 1) The Celeron II is a coppermine PIII processor with a full speed cache, your PIII 450 is not. 2) Celeron II's over 800Mhz run on a 100Mhz system bus instead of 66Mhz like older Celerons. 3) The Celeron II 850Mhz, which I recently bought and installed, can be had for $50, and Celeron II's are available up to 1Ghz at this point 4) You can continue to use your existing PC100 memory. 5) You don't have to read or understand any of the crap I mentioned in this post, or risk your components and data. The only downside is that you'll need an FCPGA to Slot1 adapter. I recommend the Asus S-370D or S-370 133. The only difference between a Celeron II 800+ and a PIII is that the celeron has half the cache, and runs at 100Mhz where the PIII EB processors run at 133Mhz.
Good Luck!
Slackmaster 2000