The most straightforward way is with .loc:
>>> data.loc[:, (['one', 'two'], ['a', 'b'])]
one two
a b a b
0 0.4 -0.6 -0.7 0.9
1 0.1 0.4 0.5 -0.3
2 0.7 -1.6 0.7 -0.8
3 -0.9 2.6 1.9 0.6
Remember that [] and () have special meaning when dealing with a MultiIndex object:
(…) a tuple is interpreted as one multi-level key
(…) a list is used to specify several keys [on the same level]
(…) a tuple of lists refer to several values within a level
When we write (['one', 'two'], ['a', 'b']), the first list inside the tuple specifies all the values we want from the 1st level of the MultiIndex. The second list inside the tuple specifies all the values we want from the 2nd level of the MultiIndex.
Edit 1: Another possibility is to use slice(None) to specify that we want anything from the first level (works similarly to slicing with : in lists). And then specify which columns from the second level we want.
>>> data.loc[:, (slice(None), ["a", "b"])]
one two
a b a b
0 0.4 -0.6 -0.7 0.9
1 0.1 0.4 0.5 -0.3
2 0.7 -1.6 0.7 -0.8
3 -0.9 2.6 1.9 0.6
If the syntax slice(None) does appeal to you, then another possibility is to use pd.IndexSlice, which helps slicing frames with more elaborate indices.
>>> data.loc[:, pd.IndexSlice[:, ["a", "b"]]]
one two
a b a b
0 0.4 -0.6 -0.7 0.9
1 0.1 0.4 0.5 -0.3
2 0.7 -1.6 0.7 -0.8
3 -0.9 2.6 1.9 0.6
When using pd.IndexSlice, we can use : as usual to slice the frame.
Source: MultiIndex / Advanced Indexing, How to use slice(None)