Before starting the installation process check my previous post about the TinyCore Linux.
1- Download the .iso file from this link. (TinyCore is just 12MB).
2- Mount the .iso file to your Virtual (CD/DVD) Drive, or from a mini-CD or even USB.
3- Open VirtualBox and make a New OS. Name : TinyCore , Type: Linux, Version: Linux 2.6 , then OK.
4- Memory Size: 256 MB, and Next
5- select Create a new virtual harddrive , press Next, and select VDI,
6- Select Dynamicaly Allocated and choose 512MB of Hard Disk and Finish.
7- Press Start button.
8- Select the drive you mounted your iso file there to start from there (for me it is E:\). Now you will see the OS loads on the RAM and you can test it but if you want to install it you need to continue the next steps.
9- On the Desktop of your TinyCore go to the Wbar (the bottom ribbon) and run APPs. It will ask about to find the fastest mirror, press OK and wait for the mirror to be find then press OK again.
10- Go to Apps>Cloud>Browse and in the search bar type tc-install and press search, when the search is complete select tc-install.tcz and press Go button. Wait to see the message: tc-install.tcz OK.
11- Now the tc-install Icon is added to your Wbar, so run it.
12- Check that the Path to the core.gz file is automatically selected (If not you have to find the file in the Mounted iso file, just double Click in the address bar to browse)
13- Tick, Frugal and Whole Disk, and choose sda from the list.
14- Press > button, choose ext4 and press > button and again in the next window press > button.
15- Then you will see in the next page the Install Extension Radio Button is checked and the address is provided. Just Press > button and in the next page you will see a brief list of all settings, you just need to press Proceed and Wait.
16- After Installation is completed. Unmount the .iso file and reboot the linux. Now it should start from the hard disk.
If you cannot do the installation process using this easy steps, then go to this link and see the super-easy installation manual.
machinelearning1 
Thanks a lot for this tutorial. TinyCore is simply awesome. I was trying to install it in vmware but it was not this much smooth.
I got it installed in VirtualBox no problem. However I am having a hard time making it accessible on the network. I am using Bridged Mode on the Network with Allow All enabled. I have set a static ip in TinyCore on the adapter to 192.168.1.150.
I then configured my router to only dhcp betweeen 192.168.1.2 and 192.168.1.90. My host has a static IP of 192.158.1.99.
I installed IpTables in tinyCore and opened EVERYTHING. Installed NGinx and NodeJs. And in the TinyCore VM I can open Chromium and browse to my NGinx website.
However from the host I cannot, and it does not respond to the ping.
Everything I can think of is configured and open (firewalls on both sides). So all I can think now is that the VirtualBox Guest Additions are needed in TinyCore to make the Bridged Nic work right. However I cannot install those because it can’t find the header files, even when I installed the header files, I need to specify KERN_DIR, and I tried pointing that to /usr/include/linux (where the headers installed to), but still no dice.
Not currently working with virtualbox 5.2.8 on a Windows host followed steps completely still crashes while booting kernel guide might be outdated for current version of tinycore
32 or 64 bits?
The installation process would be the same.