The first Wily stage is the entrance to his fortress, though curiously, unlike later games, there's no external "Skull Castle" overview.
In the first section, you'll encounter a number of Big Eyes. These guys are tough, and taking them out can be very time consuming. An alternative is to wait for them to do their highest jump, and freeze them with the Ice Slasher, simply walking under them as they stand frozen in the air. Be warned, you will still take damage if you touch them.
The Ice Slasher is also good for getting past the flame units. Freeze them as they begin going down for best results, you can use them as platforms this way, to increase the height of your jumps and clear the section easier.
You'll encounter a number of blocks throughout the stage that can be destroyed by tossing them with the Super Arm, or with the Thunder Beam. Use the former; you'll want to have plenty of Thunder Beam power for most of the fortress bosses.
Near the end of the stage, you'll come across a section with Foot Holders, with a spiked ceiling and floor. Using the Foot Holders is risky with instant death above and below you, so use the Magnet Beam you got in Elec Man's stage to advance.
After this screen, you'll come to a seemingly-impassable screen with a ladder and a huge pillar. Again, use the Magnet Beam to get over it and reach the ladder. This stage can not be completed without the Magnet Beam, so if you didn't get it, kill yourself and go back to Elec Man's stage, so you can get it. If you run out of energy, return to the previous screen and collect the capsule as many times as necessary (unlike later Mega Man games, power-ups return here when you leave the screen).
At the end of the stage, you'll meet the Yellow Devil. His body transforms into chunks of rock and he goes from one side of the screen to the other. You need to jump the low chunks and stay under the higher ones. When he fully forms, his eye will open and fire at you. The eye is his only weakness, and he can only be harmed when he is fully assembled. So use the pause/resume trick. If done properly, you can kill him with a single Thunder Beam!