A minimal base system consisting of the Apt package manager and the busybox collection of system utilities is installed when first starting Termux. Additional packages are available using the apt command:

apt update
Updates the list of available packages. This commands needs to be run initially directly after installation and regularly afterwards to receive updates.
apt search <query>
Search among available packages.
apt install <package>
Install a new package.
apt upgrade
Upgrade outdated packages. For Apt to know about newer packages you will need to update the package index, so you will normally want to run apt update before upgrading.
apt show <package>
Show information about a package.
apt list
List all available packages.
apt list --installed
List all installed packages.
apt remove <package>
Remove an installed package.

Apt as a package manager uses a package format named dpkg. Normally direct use of dpkg is not necessary, but the following two commands may be of use:

dpkg -L <package>
List installed files of a package.
dpkg --verify
Verify the integrity of installed packages.

View the apt manual page (execute apt install man to install a man page viewer first) for more information.