You do not have to do this. You just upload the new version of your program on the Android Market, and people see it right away. Users who checked the option "update automatically" for your program upgrade automatically without having to give explicit consent ; others see "upgrade available" and can just click 'upgrade' to upgrade to the new version of your program.
If for some reason you're thinking that you want to force the update on the user with or without their consent though, you just cannot do it. You can download the apk and should be able to hand it to the package manager, which in turn will ask the user to confirm whether they actually want to install it - and then again, for that you need the user to have checked the "allow unknown sources" option in development options, else the package manager will downright refuse to do it. But android will not let you install a new package without the user explicitly requesting it, or explicitly allowing auto-updates through the market.
If you have some backward compatibility issue of some sort and want to disallow running of deprecated versions of your application, you can embed in your application some logic that will check on your server for version information and terminate if it's outdated, with a message "this version is outdated, you need to upgrade to continue using this application" or something. But no upgrading in the back of the user.