BY way of a router, you need to go into the router and configure ports ( port forwarding: open the designated ports) you also need to configure the program you are using on your android (QEye for example) to work with the ports you opened on your router. IF your router is a separate unit from your modem, you are in luck . IF you have a combo router modem, you need to contact your ISP to help you set it up. Don't tell them too much about what you want to do. BY way of a dvr connected to a router, ports and passwords have to match and you must set up the dns as static. Most ISP's dont change the DNS that often and you can try and use it as if it was static. For a small yearly fee you can get a static DNS from a provider on the internet, Dyns I think is one.
BY way of the dialer, you need to put minutes on the sim card, with the right plan it costs about 20 dollars a year.
The hardest part of setup if you use the router in the system you decide upon, is configuring the ports on the router and getting the router to work with the dvr.
IF you just want to monitor an area and dont need to be notified right away if they open a door etc, they sell household objects that are actually dvrs activated by motion, so the battery will last a very long time -weeks or more.They record to a micro card. IF you get one that records to a slower fps and or resolution you can record hours of video on a 32 gig card. THese units are cheap 40 or 50 bucks -or more. THey sell all kinds of things that people would never suspect is a camera. A lot of options. Everythng you need need is on ebay for less than 100.00 plus the time you need to compare everything and decide what you need.