The trick for cheaper hotels is also similar. The most pocket-friendly option would be staying in a hostel. Especially in Europe. Another cheap alternative is AirBnb. But if your heart is set on staying in a hotel, do a comparison of hotel rates and book in advance. Sometimes, booking right before your trip can also help you land a great deal. Some of these would be non-refundable, so you might need to keep that in mind. According to most travel blogs, the best days for finding a room at discounted rates are Sundays, Mondays and Thursdays.
Happy journey!