I personally don't understand why you would want to do this seeing that you would need a very large pen drive and the performance from running anything on USB especially is horrible running a virtual OS, at least to me, doesn't make sense. But anyways here you go.
First you need to install linux onto a pendrive. There are plenty of guides out there. You can also do this on Windows. I guide for that can be found at yellowbricks.com.
Download the free ESXi ISO-image from VMware. You need to register so you can get your free licence code.
Mount the ISO-file. ( mount -o loop ESXi.iso /mnt/iso )
Extract install.tgz ( mkdir /root/esxi; tar xvf install.tgz -C /root/esxi )
Go to the directory where you unpacked the files, and then some. ( cd /root/esxi/usr/lib/vmware/installer )
Unzip the big-file. ( bunzip2 VMware-VMvisor-big-3.5.0_Update_3-123629.i386.dd.bz2)
Place this image onto your USB stick. This WILL destroy all data on the USB pen drive. Also, you need to know which device your pen drive is.
The final step will take a while since were writing 750MB of data to the USB-stick. When its finished you will have stock ESXi installation on a bootable USB pen drive. Congrats!
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