So, assuming you're with me on the West to East route, here is what happens after you get done watching the orientation video at Porteria Laguna Amarga:
Get back on your bus and put your park ticket in your dry bag. The bus will drive a scenic ~45 minutes west to its second stop, Guarderia Pudeta, on the edge of Lago Pehoe.
You and your fellow hikers will disembark the bus and walk to the catamaran (catamaran is a fancy word for a little ferry boat). The catamaran will take you across Lago Pehoe to Refugio Paine Grande, where you will begin your hike. The cost is 8,000 CLP (~$12) and you pay on-board.
Now, depending on your arrival time and the catamaran schedule, you may have some time to kill. If you have at least 35 minutes, I highly recommend going on a little hike to Salto Grande for a fantastic view of a waterfall and Los Cuernos ("The Horns"). If you have less time than that, chill in the little cafe next to the pier and use the bathroom before you board the boat.
Pro-Tip: You want to get on the catamaran almost last. Why? Because when you board everyone throws their packs in a giant pile at the front of the boat. If you get on near the first, you will have to wait forever to get your pack when the boat docks.
When it's time to board the catamaran, I recommend going to the top deck for the views. Lago Pehoe sits under the magnificent Los Cuernos and from the back of the catamaran you can get a stunning view. I know everyone loves the Torres del Paine, but for me, Los Cuernos was the mountain I came to the park to see. We unfortunately had a cloudy morning when we crossed the lake but hopefully you will have a better view!
The catamaran will dock around 1 pm at Refugio Paine Grande. You should grab your pack off the pile and begin your hike without much delay. You have 11 km (6.8 miles) of hiking ahead of you to get done before dark. It should take you 3.5-4.5 hours, depending on the wind and how often you want to stop to take in the beautiful surroundings.
This portion of the hike runs the edge of Lago Grey, where a pretty impressive glacier lies at its northern tip. That's where you're heading tonight.
When you arrive to Refugio Grey, check in at the camp office. Refugio Grey is an indoor lodge with an adjacent private campground where you can pitch your tent. Pay 4300 CLP (~$7) per person and go find a flat and dry place to set up your first camp.
Refugio Grey tends to be a little rainier than other places on the trail because Glacier Grey (which you will get to visit after you set up your tent) has its own microclimate. And that microclimate is mostly wet drizzle.
Once you have your tent set up and secured, head further afield to see Glacier Grey, which measures 6 km (3.7 miles) wide and 30 m (98 ft) high. There is a mirador overlooking the glacier about 4 km (2.4 miles) away from camp. You can choose to do the whole trail to the mirador, or just walk until you're satisfied with the view of the glacier from the trail.
When you're done looking at the glacier, head back to camp and make supper.
The Refugio Grey campground has an indoor cooking and dining room, with sinks with running water. It can get quite busy during the typical dinner hours, but it makes it easy to meet other hikers. You will be seeing these people every night for the next 4 days - you might as well get acquainted now!
Pro-Tip: If you want to take a shower, Camp Grey campground has free shower facilities. Tomorrow night you will be staying at a campground without running water or the option to shower, so plan accordingly.
When you've finished eating and washing up, get to bed. Tomorrow is going to be a long one!
Total distance for Day 1: 11 km (6.8 miles) to Refugio Grey.
You can add on another 4 km (2.4 miles) to the mirador over the glacier if you want for a total of 15 km (9.2 miles).