If you have an older emachines unit, good bet the mobo has two IDE connectors on it for the wide ribbon cables, probably right beside each other. To each of these you can attach one ribbon cable with three connectors - one to the mobo end, and the others to two devices - Master and Slave on each channel.
Both Hard Drives and CD / DVD units have been connected this way. So look closely inside. You may have one ribbon cable with one HDD on the end connector and one DVD drive on the middle connector. In that case, look for the unused second IDE socket on the mobo. If there is one, you can buy up to two new HDD's plus one ribbon cable and hook up there.
If you have ribbon cables coming out of both mobo connectors and going to two (one per cable) or three (one on one, two on the other) devices, there's still one empty connector to use for another HDD. If all four connectors on the ribbon cables are in use, I'll be surprised.
Simplest way to add a HDD is to buy the IDE type and use an existing empty connector. If your HDD does not come with instructions on how to install, connect, Partition and Format, go to the HDD manufacturer's website for free clear instructions and downloadable free software utilities to make all these jobs easier.
If you don't have an empty IDE socket or connector, or it you just want to go SATA anyway, you can buy add-on SATA controller cards that plug into a PCI slot, then hook up your SATA drive(s) to that.
IF you want to buy a drive over 138 GB (that is, by the drive guy's count that a Gigabyte really is 1,000,000,000 bytes), first check two things. The drive controller in your machine must support what's called "48-bit LBA". Note not just "LBA" - the "48-bit" part is important. Check your manual or the emachines website if possible to verify this. If your machine was made anytime after about 2000 or 2002, it's a VERY good bet you are OK here. Then check your OS - it also must support 48-bit LBA. Win 2000 did not at first, but a late Service Pack added that. Win XP original did not, but updating to SP1 or later fixes that. Vista has it in all versions.