The checklist above works for every telescope, but each design has one or two extra quirks worth knowing before the first night.
Refractors (long thin tube, lens at the front)
The simplest first night of any type: no collimation and a short cool-down. Use the included star diagonal for comfortable viewing. The image will be mirror-reversed left to right, which is normal. On inexpensive short refractors, bright objects may show a faint purple fringe. That is chromatic aberration, not a defect.
Reflectors and Dobsonians (mirror at the bottom)
Allow the longer cool-down. Glance down the focuser in daylight: you should see the small secondary mirror centered, with the reflection of the big mirror around it. If stars look like comets even at best focus, the mirrors need collimating, a five-minute job once you have done it. Tabletop Dobs need a sturdy table or crate.
GoTo and computerized telescopes
Level the tripod, and enter the date, time, time zone, and daylight-saving status exactly. Wrong time settings are the most common cause of a failed alignment. Choose bright, widely separated alignment stars. Fresh batteries matter: weak AAs cause erratic slewing, and many owners switch to a 12V power pack. Our GoTo vs manual guide explains how alignment works.
Smart telescopes (Seestar, Dwarf, Vespera)
Charge fully and update both the app and the firmware indoors on WiFi the day before. Updates in the field can take 20 minutes. Place the telescope on level ground with a clear view of the sky, not beside the house. Start with a bright target like the Orion Nebula or the Pleiades, and give live stacking several minutes to build the image.