Hopefully the donated media been kept wet since this post was so long ago...
Just cut it up and put as much of it as you can into your filter. Don't stuff the filter so full that water can't pass through, but fill any gaps in the filter with some of this stuff - fluffed up a bit. The water coming in the tank should hit this material first, and any bacteria that might get washed off will get caught by your new material.
An ammonia reading of 0.1 to 0.13 ppm isn't a huge deal. Doing a water change in this case is a good idea, but it isn't

worthy.

That type of reading is considered "good" during a fish-in cycle. If it gets higher than that, like 0.25ppm then it is more like

, but 0.1 is more of a

.
Just do the water change and wait another 24 hours. If the material you got from the LFS has been kept wet, you may find yourself "cycled". If that is the case, you will find nothing but double zeros from here on out. If it is, leave the old stuff in the filter. I would slowly take little bits of it out of the filter each month. Just a little at a time, until 6 months from now it is all out. The bacteria will have colonized your filter media and then you are good to go. You can use the scraps you are pulling out to give to friends who are starting tanks, or just toss them. Eventually you will need to change over your media as well. (Not for quite a period of time though... talking about years here, not weeks like the filter makers will tell you.) You would want to follow a similar formula when doing that. Take out the old media and keep it wet in a bucket. Put in the new material. Cut up the old and put it back into the filter. The bacteria will colonize the new from the old. You won't have a new cycle, because you will have a fully functional biofilter the entire time.