If you are on an extreme budget but want to see the world, here are a few ideas.
Nearly every city in the world has a hop-on-hop-off bus that will take you all over town, and allow you to stop anywhere you want. You can take time to see a site and get back on the bus when it comes around again. You purchase a day ticket.
A city-run bus is another way to see the city. Get a round trip ticket and ask for a transfer that you can use on another route.
Don’t be afraid of the program, Couch Surfing. These are folks who will open their home to you for a few days. It is usually for three nights and is always free. The host/hostess may take you around to see the local area, or let you go on your own, with their instructions on how to get there and return. Host/hostesses are reviewed at the end of the stay and they review you, as well. This is posted on the couch surfing site for all to see.
Hostels with kitchens can save you money, from not eating out at restaurants. Purchase food in local grocery stores and cook it in the hostel.
If you do eat in restaurants, it’s often cheaper and a lot more fun to get meals in local neighborhoods. Ask folks for the best local restaurant.
Travel light and purchase change of season clothing in thrift shops. That way, it’s not a waste to leave them behind when you leave.
Local libraries are always free and may have lists of free community activities, as well. Go to the free community activities and really see how the locals live.