I am installing ESXi for the first time and really need to know if I have to partition and format the hard drive for the virtual machines prior to installation of ESXi or ESXi will be handling all hard drive problems for me?
short answer: don't worry. No need to partition.
longer answer: make sure that there is nothing you are still interested in on the hard disks attached to the hosts you install ESXi on when you install. ESXi will apply a default format for it's own (management) stuff, and create a "data store" from the space left.
remark on namings:
ESX and ESXi store hypervisor "stuff" they need to run on partitions usually not visible in the VI Client. You get to see results that come from there, like log entries, but usually you are not moving around there by yourself (unless you explicitly login the the CLI on the ESX host). Such partitions are often locally attached disks on a ESX/i host, as they are only used by one single host.
Virtual machines and such are stored on separate partitions, called "data stores", and usually you put those on a shared storage so everyone attached to the SAN/NAS can see and use the data store. However, data store can reside pretty much everywhere - also on local hard disks. In that case, other host would not be able to mount that data store, but it's still a perfectly avlid data store.
To share locally attached disks with other ESXi hosts, have a look at the vSphere Storage Appliance.
Yes, ESXi partitions and formats vmfs volumes on your local disk.
During the reboot operation, VFAT scratch and VMFS partitions are created on the disk.
The "hard drives" you set up for Virtual Machines are actually files. Usually VMDK files with VMWare. Your physical hard disks become Data Stores and as you configure virtual machines and drives for them, you'll see folders with various files, the largest of which will probably be VMDK files which are the only Hard Drives the virtual machines know about.
So don't bother partitioning anything on the physical drives. Do all your hard disk config for the virtual machines inside the vCenter app as you set up each virtual machine.