These are the steps if you are installing a system apk for Android 5.0 or later devices. For older versions use posaidong's answer
Rename your apk file to base.apk
$ adb push base.apk /sdcard/
Enter the console and get the shell
$ adb shell
Switch to superuser. If your device is not rooted, get it rooted first. (If you don't know how to do that, just Google.)
$ su
Remount the system partition with WRITE permission.
$ mount -o remount,rw -t yaffs2 /dev/block/mtdblock3 /system
Create a Test directory inside /system/app folder. (or can use /system/priv-app as well). Ideally this folder name should be application name. For now, lets use Test
$ mkdir /system/app/Test
Requires 755 permission for this dir
$ chmod 755 /system/app/Test
Copy your base.apk inside
$ cat /sdcard/base.apk > /system/app/Test/Base.apk
Remout /system partition back to READ-ONLY, and exit
$chmod 644 /system/app/Test/Base.apk
Requires 644 permission for this dir
$ mount -o remount,ro -t yaffs2 /dev/block/mtdblock3 /system
$ exit
Reboot your device. When boot completes you should see a system message like Android updating ...