She has a Compaq Presario S3300NX. Using this link:
Memory Finder
... can she buy a 1GB RAM and have me install it? I had such good results on my computer after following advice on here that she wants to give it a shot as well :)
If I'm reading it right, she can upgrade to ONLY a 1GB, correct? Can she buy one chip/1GB or should she buy 2 chips/512MB each?
Also, I think it says she needs 400MHz... will it hurt her computer if it goes down to 333MHz or goes up to 667MHz?

From your link, it appears correct. Before you buy the memory, look inside the computer and note how many empty memory slots it has. The link says there should be two slots. If she already has 1GB of memory, you can't add any. If she has less, but the slots are full, then you can replace one or both memory modules. If there is a free memory slot, you can add up to 512 megabytes.

You can also find these at Crucial Computer memory upgrades for HP - Compaq Presario S3300NX Desktop/PC from Crucial.com or Kingston Kingston Technology Company - Kingston Memory Search - Search Results for:. The price at Crucial is better. I've had good luck buying from either of these companies in the past.

She can't buy 1GB chips, just 512 MB chips. If she needs 400 MHz memory, she can use 667 MHz memory (faster is ok), but slower, 333 MHz is not recommended (it might work; it might not). Faster memory can be accessed faster. The clock speed is what determines the actual speed. If the memory clock speed is too fast for the memory, there may be some errors.

When you put them in, make sure they're fully seated. If the system doesn't recognize the memory when you turn it on, turn the system off, pull out the memory and try reinserting it.

One more thing: Crucial is showing a PC2700 as being compatible. Now, I bought the RAM for my computer off eBay and had great luck, so I was looking around on there. Would these work for my friend's computer?
Crucial 1GB KIT DDR PC3200 DDR DIMM 400MHz Unbuf NoECC - eBay (item 260405834861 end time Jun-05-09 02:18:19 PDT)
It has a different part number than what Crucial is listing as compatible - however, the ones on eBay are PC3200, not PC2700. Can I get the ones on eBay without worrying?

PC2700 is the same as DDR333 memory. PC3200 is the same as DDR400 memory. If the pins are the same (they appear to be) the PC3200 should be compatible.

One more thing: what's the difference between non-ECC and ECC? If her computer is supposed to take non-ECC and we get ECC chips, what will happen?

OK here we go...
You/She has a Compaq Presario S3300NX.

Does the Compaq Presario S3300NX support ECC? NO. NON-ECC is cheaper and should run a little faster. ECC (Error Correcting Code) memory is parity memory and non-ECC memory is non-parity. Parity memory has an extra chip on the module that checks for errors in the transfer of information to and from the memory. So if a memory module has an odd number of chips, it is parity RAM.

Does the Compaq Presario S3300NX support dual channel? NO. Don't pay more for a matched set.

The Compaq Presario S3300NX has 2 memory slots. The MAX you can put in each slot is 512MB.

OK now the speed.
PC2700(DDR333) is slower than PC3200(DDR400). Note: at the same CL rating. (184 pins).
Note: DDR memory is backward compatible. Meaning a PC that needs PC2700 memory could use PC3200, it will just only run at a PC2700 speed.

SO, what are MY recommended specs for you?
2 modules of PC3200 (DDR400), 512MB each, and a CL of 2.5 HERE

I hope this helps.