Once the sun sets you aren’t allowed to eat or drink (except water) until you make Havdalla (in tefilla and al hakos). The exception is Shalosh Seudos – you have until a half hour before tsais hakochovim. (ShA 1 – MB 1, 35)
If you began to eat (said Hamotzi) while you were allowed to, you may continue your meal even after dark. (ShA 1 – MB 2)
If you were just drinking, not in a seuda, you must stop by shkia. Say Havdalla and then go back to drinking. (ShA 1 – MB 5 – BeH “tzorich”)
Are you allowed to drink the kos shel beracha of Shalosh Seudos? If it is bain hashmoshos, yes. If it’s already dark, no – save it for the Havdalla that you will say after Maariv. (ShA 4 – MB 14 – BeH “m’voraych”)
Someone who always benches on a kos shel beracha is allowed to drink the cup before Havdalla. (MB 14)
What if you forget to make Havdalla? After Shabbos, you have until Tuesday evening – do it as soon as possible and no eating until then. After Yom Tov, you have all night. Rabi Akiva Eiger held that you can make Havdalla the whole next day after Yom Tov. (ShA 6 – MB 16)
When you say Havdalla after Motzo'ay Shabbos, omit the beracha on the ner and on the b’somim. (ShA 6)
If you want to have a bread meal immediately following Havdalla, do not bring out the bread until afterwards. If the bread was already brought before Havdalla, cover it until after Havdalla since the beracha on bread normally should precede the Hagoffen on wine. (ShA 9)
You aren’t allowed to do melacha (even d’rabbonons) before Havdalla. If you said Havdalla in tefilla, it is good enough. If you need to do melacha before Havdalla, say “(Boruch) Hamavdil bain hakodesh u’vain hachol” first. (ShA 10 – MB 32, 34)
Women who do not daaven Maariv should be trained to say “Hamavdil bain kodesh l’chol” before doing melacha. (Rama 10)
When Yom Tov falls out on Motzo'ay Shabbos, do not begin to cook etc. until you say “Boruch hamavdil bain Kodesh L’Kodesh”. If you said Vatodianu in tefilla, it's good enough. Even still, no eating until after Kiddush. (MB 36)
Once it gets dark on Yom Tov Sheni, you can begin preparing even though you did not yet daaven Maariv nor say Kiddush. (MB 40)
The Maharil would fold up his tallis every Motzo'ay Shabbos in order to be involved with a mitzvah right away. (MB 40)