"Cutting the new chain" = The new chain will be several links too long and require that you figure out how long it should be and remove the extra links.
Then use the same tool to push the pin in place (while it's on the bike) to connect the new chain.
Chain tools sold in your local bike shop will work on all but the most exotic chains (a campy 11-speed takes a $150 tool).
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My C&V Bikes:
1972 Bottecchia Professional, 1972 Legnano Olympiade Record,
1982 Colnago Super, 1987 Bottecchia Team C-Record,
1988 Pinarello Montello, 1990 Masi Nuova Strada Super Record,
1995 Bianchi Campione d'Italia, 1995 DeBernardi Thron