The first step to decoding the signal is to find your remote control on the LIRC website.
Then, once you've found it, you'll want to examine the header, ONE, and ZERO bit durations.
Just to use an example, you can see for this random remote, the duration buffer will have two initial bytes of +2474 and -532 (or thereabouts). You'll notice that this database logs ON and OFF durations in order with the first number to be presumed to be a "high" signal and the second number to be presumed to be a "low" signal. The Tessel API disambiguates by returning positive numbers for a high signal and negative numbers for a low signal. Then, for each pair of durations after the header, a +1266, -532 pair will be a "1" and a +666, -532 will be a "0".
So, for example, to signify a buffer of [1, 1, 0, 0, 1, 0], the actual durations will look like:
<2474, -532, 1266, -532, 1266, -532, 666, -532, 666, -532, 1266, -532, 666, -532>
Or, in signed, 8 bit hexadecimal form that Tessel represents buffers with:
<Buffer 09 aa fd ec 04 f2 fd ec 04 f2 fd ec 02 9a fd ec 02 9a fd ec 04 f2 fd ec 02 9a fd ec>
I should also note that detecting IR signals can be pretty messy (depending on reflections, sunlight, etc.) so your recorded durations will be slightly off from expected. You'll need to take into account some amount of error.
Does that make things more clear?