Splicing's not to difficult, just a bit fiddly with cassette - it was much easier with reel-to-reel. The hardest bit is usually opening and reassembling the cassette!

Get the proper adhesive tape if you can.

It's important to put the adhesive tape on the "back" of the magnetic tape - the "shiny side".

The "no tools" recipe:

Place one of the "broken" ends on a plastic sheet - the cassette box will do. "dull" side down, shiny side up. Hold in place with a couple of small pieces of splice tape - one at the end and one about an inch along.

Place the other "broken" end on top, shiny side up, overlapping slightly. You want to overlap just enough to ensure that there is an overlap of "good" tape, not stretched or twisted. Tack this in place temporarily with another 2 bits of splice tape. If you have just pulled both ends out of the case, make sure the tape is not twisted.

With a scalpel (or razor blade) cut through BOTH tapes at 45 degrees. Remove the waste end from the top tape, don't worry about the one underneath.

Use a small piece of splice tape - about 10-15mm - across the diagonal cut to stick the ends together. Rub it down with your fingernail.

Trim the edges of the splice - take off any overhanging adhesive tape, with a tiny sliver of the brown magtape. This ensures that adhesive residue won't get on the tape heads.

Remove the bits of tape you used to tack the tape in place, discard the "underneath" offcut, and reassemble.