Church Records in Canton Appenzell Ausserrhoden
Similar to the situation in canton Bern (see here) Swiss residents can view church records for canton Appenzell Ausserrhoden on familysearch only from Family History Centres. There are two differences to Bern: familysearch does not indicate that the records can be viewed on the State Archive website - but there are also good news: the scans on the State Archive web site are more recent, with higher resolution and in colour. So - even if you can access data on familysearch from home, I suggest you have a look on the State Archive images.
The list of parishes on the State Archive web site is not alphabetical - on https://kb.ghgo.ch/images/docs/KB-AR-dig.pdf you'll find the parishes and links in alphabetical order, together with the earliest year plus the parish to check for even earlier events.
Please, let me also mention Geneal-Tree, a gedcom database with a fair number of entries in canton Appenzell Ausserrhoden, especially families of Gais or related to families in the Toggenburg Valley of St.Gallen. The "Erweiterte Suche" allows to define extensive search criteria.
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Whilst the example in Council minutes Chur 1889: transcription, translation and background explanations is coming from Graubünden, not Appenzell Ausserrhoden, it may also be of more general interest:
1) It deals with a one-page handwritten text and provides a line-by-line transcription (gives you a chance to practise reading the script) plus a translation - with a few terms which cannot be just translated, but need further explanation.
2) If you scroll down you'll find some explanations, which also apply to the situation in canton Appenzell Ausserrhoden: basic rules of Swiss citizenship, difference between "Bürgergemeinde / Bürgerort" and "politische Gemeinde", differences between "Zivilstandsregister", "Bürgerregister", "Familienbuch", "Familienregister". Terms one should be familiar with if researching in Switzerland.