In Mass Effect: Andromeda, the mission begins with you. Though your character will always be one of the Ryder twins, human children of Pathfinder Alec Ryder, there are still a few choices to make. You can customize your appearance, choose your gender, and specify which gender Shepard was in your universe. The most immediately game-affecting choice, however, is your choice of training. This doesn't have to be a live-with-it-for-the-rest-of-the-game decision like choosing your class in the previous Mass Effect games, but it will determine what powers you have access to during the early missions.
If you've played Mass Effect before, I recommend the Scrapper (read: Vanguard) or Operative (read: Infiltrator) backgrounds- they give you more tactical options than the basic run & gun.
The last choice is difficulty level. As in previous Mass Effects, this is only effects combat, and will not change the story. Note that the 'Insanity' level is available in your first playthrough.
Once you've made your selection, it's onward to Andromeda!
You'll wake up from cryo and engage in a little small talk with the staff. This introduces the new 'tone' dialogue system. Similar to Dragon Age: Inquisition, this lets you choose the tenor of your response, rather than its moral value. While the pattern of your choices will eventually shape Ryder's personality and future dialogue options, there's little immediate consequence to choices in the prologue, so just pick what you like.
A brief zero-g incident will introduce you to the basic commands. When you're back in control, check in on your brother, then explore the area. There are people to talk to, and items to inspect if you want to brush up on your lore (the information wall in particular has a few screens worth of recap).
Mercifully though, there's no achievement tied to getting every single journal entry (and you'll be back here later anyway), so when you're done inspecting cryopods and reading data pads, follow your objective marker out.
The next room is an introduction to your scanner. The main thing to know is that the scanner is very short-range- you can only analyze things that are right in front you.
Activate it with [G] and use it on the left bank of machinery here to reveal the components. Hold down the right mouse button to scan them, and reveal the faulty component, then Use the power terminal to reset the relay.
There are more miscellaneous items to examine in the next section, but again nothing groundbreaking or achievement worthy.
When you're done scouting, join Cora in the tram and activate the panel for a quick ride to Cutscenesville.
Again, chose your dialogue as you like, eventually regaining control in the locker room before launch.
Follow the markers to gear up, and explore the room for more personal touches and interaction. You can talk to the team, mess with the radio, and touch the lucky rock in the corner.
When ready, join the launch, which doesn't quite go as planned. By the time you regain control again, you'll be standing on an alien world.