When you look at the information window of a weapon module, you will see accuracy falloff and optimal range. These attributes tell you how far you should try to be away from your enemies.
If you can keep an enemy at exactly the optimal range of a weapon, then that weapon will theoretically never miss that enemy. However, if your weapon's tracking speed is too slow to keep up with the moving enemy, then it might miss the enemy even if you're at optimal range for that weapon.
Accuracy falloff tells you how far away your weapon can be from optimal range and still have at least a 50% chance of hitting the enemy. So, if your weapon's optimal range is 10,000m and your accuracy falloff is 3,000 m, then if you are 13,000m away from the enemy, your weapon will have about 50% chance of hitting the enemy.
Two times the accuracy falloff plus the optimal range is the distance at which your weapon will always miss the target. So, continuing from the above example, if you are 16,000m away from the enemy, your weapon will not be able to hit the enemy at all.
Tracking speed is a measure of how quickly a weapon is able to rotate. Angular velocity is a measure of how quickly an object is rotating, relative to your ship. If your weapon's tracking speed is significantly lower than the angular velocity of your enemy, then you will have a low chance of hitting that enemy. At the same time, if you have a high angular velocity relative to your enemy, the enemy will have a low chance of hitting you.
The signature resolution of a turret is a measure of how big a target has to be for that turret to hit it accurately. The signature radius of an object is a measure of how big or small it is (or appears to be, to a turret that is tracking it). If your turret has a small number for its signature resolution, that means that the weapon will be able to hit small objects pretty effectively.
The tactical overlay is a view that you can turn on while you're in your ship by pressing the button with the target on it to the left of the capacitor. It shows concentric rings centered on your ship.
The concentric rings denote the distance, in km, from your ship.
When you hover over a weapon turret or other type of module restricted by distance, a sphere or two will appear around your ship.
If you see two spheres around your ship, this means that the turret that you are hovering the mouse cursor over has an optimal range and a falloff range.
The inner sphere always shows your optimal range. Enemy ships on or near that sphere are in your optimal range, where your turrets have the best chance to hit them. It doesn't affect how much damage you deal; it just denotes how likely your weapons are to hit the enemies.
Your turret tracking speed will also affect how likely you are to hit the enemies, to the point that even if a ship is in your optimal range, you could still miss if the ship is circling you faster than your turrets' tracking range. In other words, optimal range is by no means a guarantee of hitting the target.
The outer sphere represents your optimal range plus falloff range. Ships that touch this sphere or are outside of it are extremely unlikely to get hit by your weapons.
To fight another ship in EVE Online, you must target that ship, keep the ship at the optimal distance from your weapons, if possible, and keep your defenses up while shooting at the enemy. Your ship computer will automate many of the tasks that you need to do while fighting, like keeping your ship at the appropriate range, but there are still some tasks that you need to do to engage in battle with another ship. This article explains how to do that.
To target an enemy ship that you want to fight, just click on the enemy, either in the nearby objects window, or in the view of space, and then, in the selected item window, click the target icon. A quicker way to target the enemy is to right-click on it and choose Lock Target.
To be able to target an enemy, the enemy must be in targeting range. You can find out the targeting range of your ship, look in the fitting window. The targeting range is listed on the right. You can also turn on the tactical overlay, which is the round button with the target on it that is to the left of your capacitor and hit point meter, and if you zoom out, you will see a bubble around your ship. If you do not mouse over any of your weapons, the bubble represents your targeting range. You will not be able to target ships outside of that bubble.
It helps to always be familiar with the optimal range and accuracy falloff values for each of the weapons that you have fitted to your ship. The optimal range is the distance at which your weapon damage is most likely to be at its most accurate. The accuracy falloff is the distance from the optimal range at which your weapon starts to lose accuracy. If you cannot keep the enemy at your optimal range, then try to at least keep the enemy within the optimal range and the accuracy falloff.
The Selected Item window has a Keep In Range button that looks like a diagonal line with two arrow heads at each end. When you click this button, your ship's computer will attempt to keep your ship at the specified distance away from the selected item. You can select the distance that you want to keep in range from your enemies by right-clicking on the Keep In Range button; you will then be prompted to type in the distance, in meters, that you want to remain away from your enemies. This is a good way of ensuring that you keep your enemies in the optimal range for your weapons. Remember, if your preferred distance is in kilometers, 1km = 1,000m.
After pressing the Keep In Range button, your ship will automatically adjust your speed and trajectory to keep you at the right distance. Double-clicking in space or otherwise changing your trajectory manually will disable the Keep In Range, so you will have to click it again if you want to Keep In Range again.
The tactical overlay, as described in the above section, will show you two bubbles in addition to the targeting range bubble when you mouse over a weapon. The two bubbles are your optimal range (the smallest bubble) and your accuracy falloff. Ships that are exactly on the edge of the smallest bubble will be in your optimal range, meaning your weapons will work the best on them at that distance. At the accuracy falloff (the bubble outside of the optimal range bubble), your weapon starts to be less accurate. If your distance from the enemy is twice the distance between you and your accuracy falloff, your weapon will probably not successfully hit the enemy at all.
Because of the way that combat works in EVE Online, it is usually harder to hit an enemy that is rotating around you if you are using turrets. This is because turrets need to rotate in order to "track" the enemy. A weapon's tracking speed determines how quickly the weapon can rotate to keep following the enemy. If you orbit around an enemy at your deired range instead of using the Keep In Range button, and if the enemy is using turrets, you might reduce the damage that the enemy does to you somewhat. However, if the enemy is also trying to rotate around you, your weapons will also have reduced accuracy, especially if they have low tracking speed. This can be helpful, however, for slowing things down in battle a little bit.
If needed, activate non-passive defenses like an Invulnerability Field, Damage Control, and so on. These defenses help with tanking, which is the act of managing your ship's defenses to reduce damage as much as possible. Some types of NPCs use weapons that tend to cause specific damage types, like EM damage, Kinetic damage, and so on. If you know what type of damage your enemy is likely to inflict upon you, you might want to consider investing in defensive modules that strengthen your resistances to those types of damage. There are also skills that increase resistance against those types of damage.
Once you're ready to fight the enemy, if you have the enemy targeted, select that enemy and click the weapon, and the weapon will automatically start shooting at it. You can also just click the weapon and then click the ship that you want to shoot at.