You can access your data via the dataset number. Using a Python kernel, you can access dataset number 42 with handle = open(get(42), 'r').
To save data, write your data to a file, and then call put('filename.txt'). The dataset will then be available in your galaxy history.
When using a non-Python kernel, get and put are available as command-line tools, which can be accessed using system calls in R, Julia, and Ruby. For example, to read dataset number 42 into R, you can write handle <- file(system('get -i 42', intern = TRUE)).
To save data in R, write the data to a file and then call system('put -p filename.txt').
Notebooks can be saved to Galaxy by clicking the large green button at the top right of the IPython interface.
More help and informations can be found on the project website.
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