I have been given an Athlon 1Ghz Processor of only 1yr old and I would like to know if I can swop it over with my AMDuron 601Mhz without having problems. My MotherBoard is a LEX BN780 Via KT-133 chipset

Probably. Drop it in and try it out. If it doesn't work, a BIOS update from the motherboard manufacturer will probably fix the problem.

Is it an easy thing to fit ?

Yes it is. As long as you are comfortable with the inside of your computer.

Buy a new cooling fan. Any local computer retailer can point you in the right direction. Tell them you need a quality cooling fan for a Socket A 1ghz Athlon. Verify that it comes with heat conductive compound, or buy some.

Here is a direct link for some how-to videos on the AMD website:
http://www.amd.com/us-en/Processors/TechnicalResources/0,,30_182_869_1073^6678,00.html

Find your motherboad manufacturer's webpage and check out the specs for you board before finding out the hard way that it can't take the chip. (No need to swap CPUs till you KNOW it can take it.)

Good Luck!

CPU are very easy probly easier than a stick of ram to fit on a dimm slot. That is if you have the zero insertion force (ZIP) upgrade slot. If you open your CASE look at your MOBO and look at the processor area. The slot should have a stick like handle to the side of the SLOT. Pull that up and your old processor is out. After that put your new one in and pull it down. The new processor is fitted in. You cannot put it in the wrong way for the design of the processor forbiddens it. It has specific matching spots. Put on your grease on the CPU die usually comes out on the cpu as a black spot. Then Your grease on your cooling most likely an aluminmum or copper round circle. Apply it as even as possible. Then fit your fan. Although your CPU is the easiest thing you can fit fitting the stupid fan and its heatsink is the hardest thing if you have a poorly designed heatsink.

After CPU is fitted in start your computer. Go into your BIOS and load failed default. Also I would recommend clearing your CMOS before doing any CPU upgrading.

What are CMOS ?

DO NOT clear your CMOS before you upgrade your CPU. There is NO reason to and you loose all your BIOS configuration settings. The BIOS will pick up the new CPU on it's own and reflect that change for you in CMOS.

CMOS is basically what holds the configurable settings for the BIOS. When you boot your computer and go into the BIOS settings, you are actually going into CMOS.

CMOS information is maintained from a charge from the CMOS battery on the motherboard, whereas BIOS is a ROM chip on the motherboard and is not erasable. (Technically BIOS is an EPROM so you can flash it to upgrade it. EPROM = Erasable, Progammable, Read, Only, Memory)

If I missed anything I am sure someone will correct me. ;)

To J5im8yo:

Stick with asking questions, not supplying answers - you're not ready yet. Clearing CMOS is NOT necessary in this case & was a stupid suggestion. BIOS default settings are not good performance settings & if you don't know what needs to be reset after the CMOS clearing, the system will run like crap!

Compound
Metal
Oxide
Semiconductor