The cardiac cycle can be confusing at first, however it's important to remember that the heart is a muscle and so to carry out its function it has two main steps; diastole (relaxation) and systole (contraction), just like any other muscle.
Visualise the heart as a square with four chambers separated by a +. The top half are the atria and the bottom are the ventricles. For the purpose of this explanation I will just talk about the right side of the heart (the left is exactly the same, I just don't want to confuse anyone with different valve names)
1. VENTRICLE DIASTOLE (EARLY): During diastole the ventricle relaxes, equalising pressure and so blood enters the atrium from the vena cava (the main vein) and fills it.
2. VENTRICLE FILLING (LATE DIASTOLE): When the pressure gets too high the valve (tricuspid valve) between the atrium and the ventricle is pushed open, like a door, allowing blood to rush into the ventricle.
3. ATRIAL SYSTOLE: Meanwhile the sinoatrial node (SAN), which is the battery of the heart, sends out electric signals across the atria. This signal causes the atria to contract and force even more blood into the ventricle until it is packed full of blood.
Note that this causes the pressure to rise in the ventricle so much that the tricuspid valve is forced shut with a LUB (the first sound from the LUB DUB heart sounds) , just like wind slamming a door shut
4. VENTRICLE SYSTOLE (EARLY): Remember that signal from the SAN? Well it's back- it has now spread from the atria to another node between the atria and the ventricles called, funnily enough, the atrioventricular node (AVN), which conducts the electric signal along nerves (Purkinje fibres) running down the centre of the heart (the septum) and into the ventricle muscle causing an enormous contraction!
5. VENTRICULE EJECTION (LATE SYSTOLE): This electric signal causes the ventricular muscle to contract with incredibly high force, pushing large volumes of blood up and out of the ventricle through the pulmonary valve
And then everything relaxes again, allowing the atria to fill and the pulmonary valve is slammed shut due to pressure, creating the DUB from LUB DUB heart sounds.
So to summarise: ventricular diastole fills atria --> ventricular diastole fills ventricle --> atrial systole fills ventricle that tiny bit more due to SAN signals --> ventricular systole due to AVN signals causes muscle contraction --> ventricular systole causes blood to be ejected --> and then ventricular diastole again!
A diagram would simplify this more, let me know if you would like one!