Multi Tag Search
In the search box, enter the tags you are looking for in this format:
This will return any spring in the notebook that shares those two tags. In situations when you have multi word tags, wrap the words in quotation marks like this:
#tag1 #"tag word2"
This works the same as just the tags but allows for multiple words.
Springpad no longer offers a specific feature for saving advanced searches, but there's no reason you can't use a work around to accomplish the same thing. Once you have run a search in a notebook and have your results, either bookmark the URL for the page or copy it and paste it into another note. In either case, that new URL will now return a result page based on that search each time you use it, but it will contain the current notes at that time.