1. Open Fritzing
2. Part window is on the right of Fritzing window, go to Core parts
3. In "ICs" section, select the first one - with "IC" on it
4. Inspector window is right under the Parts window (if not, go to Window->Inspector), we need the Properties section
5. In that section, you can select your package type (DIP/SIP/various SMD options), variant, number of pins and even label your IC any way you want.
6. Edit the pin labels.

Everything is autogenerated. For even better effect, select the part and go Part->Edit . I didn't even need that to make an ATTiny.

Problems:

1. I don't know if a part like this is easily distributable, didn't find any button to export a part (I saw one candidate but it was greyed out).
2. I didn't see any setting to make a wider DIP footprint (as in - for bigger ICs) like old CPU/RAM/ROM chips etc. It probably can be done the "part from scratch way", but the setting might also be already there.