accommodation
Staying in a hostel will be your cheapest option.
Apps like hotwire, kayak, expedia for hotels. Be very specific about what amenities you are looking for.
Taking an overnight bus or train to a new destination, saves on accom - understand it wont be fantastic sleep.
food & bev
Take snacks & (lunch?) from the included hostel buffet. You pay for the food & lots of other travelers do the same!
Eat like a local, especially where there are unique cuisines, you might find a new favourite.
Make sure that you have a re-usable water bottle (& filter if necessary).
Hostel happy hour hits different.
transport
Set up email notifications for sales of flights or trains that you are considering taking.
Flexibility in departure dates
Look into transport cards in the destination
Swapping miles for flights. Some credit cards are a great deal when used wisely
activities
Hostel activities - generally heavily discounted
Get your steps in, that way you won't miss hidden gems - bonus points it's free
Free walking city tours - meet friends & tip based!
Booking early for museums or galleries, save money and time in line as well!