To get internet access to work on Mac OS 8.1, I used this guide written by Clockwise for Emaculation.com.
The following are the specs of my emulated Mac:
• Hard drive image in .dsk format with Mac OS 8.1 installed
• Macintosh Quadra 950 ROM
Here are the steps I took:
• Selected the '68040' CPU and 'Quadra 900' Mac Model ID in the 'Memory/Misc' tab and 32MB RAM
• Selected 'Internet (slirp)' in the Basilisk II config page 'Network' tab
Then on a Mac OS 8.1 volume, check for the following:
• Using the Extensions Manager, start with minimal extensions by selecting 'Mac OS 8.1 base'
• Make sure all four 'Open Transport 1.3' 68k extensions are in the Extensions Folder
• Delete the 'MacTCP DNR' file from the System Folder and TCP/IP prefs in the Preferences Folder
• In TCP/IP, select connect via 'Ethernet' and configure 'Manually' and type-in the IP and DNS numbers (see below)
• Restart the Mac and launch your browser, i.e., iCab 2.9.9
The numbers needed to be entered in the TCP/IP control panel are:
• IP Address: 10.0.2.5
• Subnet Mask: 255.255.255.0
• Router Address: 10.0.2.2
• Name Server Address: 10.0.2.3
With the same settings as above, I got Internet working with Mac OS 7.6.1 by downloading and installing Open Transport to 1.3 and then manually updating the files to 1.3.1:
• The Open Transport 1.3 (Gold Master) from the MG, then
• Manually replaced the Open Transport 1.3 files to 1.3.1 with Open Transport 1.3.1 Update For OT 1.3 68k
Note: both the Open Transport installer and 1.3.1 update files should work on System 7.1 through Mac OS 8.1 . As noted by Dan Palka, Mac OS 7.6.1 runs faster than Mac OS 8.1, which was true for me using Basilisk II.
For reference, Here's an image the TCP/IP control panel with the right addresses: