Since you just installed today, do the installation again. While you can recover from this, it'll be a lot more work than redoing the installation.
To recover from the deletion of
/usr/bin, you would need to reinstall all the packages that have files in that directory. You can use this command to list the affected packages:
grep -l '^/usr/bin/' *.list | sed 's/\.list$//'
You'll then need to find some way of downloading the packages without relying on any of the deleted programs. Since you've deleted
dpkg, the low-level package installation utility, you'll need to obtain it from somewhere first. Grab it from some other machine running the same release Ubuntu, or download the
dpkg package on another machine and extract the programs from it. You'll need not just
/usr/bin/dpkg but also all the other programs in that package, including
update-alternatives and all the programs named
/usr/bin/dpkg-*. Again, copying might be tricky with so many programs deleted, so you may need to reboot to a rescue CD/USB to do it.
Once you have the
dpkg suite, download at least the
apt package somehow, perhaps on another machine or in a still-running web browser.
apt manually with the command
dpkg -i /path/to/apt_0.8.16~exp12ubuntu10.2.deb
If you get errors about missing commands, reinstall the corresponding packages first. Then reinstall all the affected packages:
apt-get --reinstall install $(grep -l '^/usr/bin/' *.list | sed 's/\.list$//')
Again, in your situation, just do a complete reinstallation.