Each stage of Gradius is composed of three sections: the pre-stage, the stage itself, and the post-stage boss fight.
The pre-stage is a space-only section where you are free to any location on the screen without fear of colliding with the terrain. During this section, you will be attacked by squadrons of basic flying enemies, most of whom are likely to deliver power-up capsules. Capsules can be obtained from two types of enemies, the formation types which only provide power-ups if you destroy every member of the formation, and the alternate red colored enemies which always leave a capsule behind if destroyed. If you are starting with little to no power-ups, this is your best opportunity to increase your firepower before the stage begins in earnest. The best power-up strategy depends on both your style of play, and the stage that you are about to enter. Stay mindful of the highlighted position on the power-up bar. If you allow the bar to switch from Shields back to Speed Up, and you don't have shields, you may have wasted six capsules. Read the power-up strategy guide in the "How to play" section for more information.
Each stage is different from one another and contains numerous unique aspects. The stages are covered in depth on their own pages in this guide. Note the inclusion of Stage X between stages 4 and 5, which is unique to the PC-Engine version of the game. You will not encounter this stage in the other versions of the game, including the original Arcade version. Similarly themed, but entirely different stage also exists on the MSX and Commodore 64 version of the game.
At the very end of every stage prior to Stage 6, you will encounter the post-stage boss fight. This fight consists of a battle with a unique stage sub-boss, followed by a showdown with the Big Core. The Big Core is the same on every stage, so the strategy will always be similar from one encounter to the next. When the Big Core arrives, it's core is shielded and no portion of the craft is vulnerable. When the shield around the core dissolves, the barriers directly in front of the core become susceptible to damage. You must then begin to shoot and destroy each of the four barriers until the core is exposed to your weapons. Then you must shoot the core until it explodes, destroying the craft. If you take too long to shoot the core, the core will turn red, and you will no longer be able to destroy it. After the core turns red, the craft will self-destruct after a number of seconds. All the while, you must avoid laser fire from its four laser cannons. The Big Core flies up or down depending on your position relative to it. You can force the Big Core to fly between two specific positions by moving back and forth between laser fire, and shoot at the core between bursts.