To run ESXi on VMware Workstation, use this KB article - VMware Knowledge Base
Other than that, there isn't a way to use vSphere locally on your laptop unless you want to load ESXi directly on the hardware and blow away your Windows OS install (I'm guessing you don't want to do that).
There are people who install it on desktops, connect the video card to a Windows VM, and hook their monitor up to the output of the video card, thus giving a "native" experience from the Windows VM. You would also have to pass through USB devices in order to have input working. I wouldn't recommend trying that setup if you aren't familiar with the hypervisor yet. PCI passthrough might not be available in the free ESXi. The motherboard also has to support IOMMU for PCI passthrough to work.
But if you have any spare desktop hardware sitting around, chances are it will run ESXi (network card and drivers could be a sticking point on this one), and you could load it there natively, but manage it from your laptop.
Overall, I recommend getting Workstation and following the KB listed above. Once you have it installed, you can access the Host Client by browsing to https://[esxi-server-address]/ui and looging in with the root username and password. From there, it's off to the races.
