darse cuenta vs realizar
'Realize' in English means to notice, but realizar in Spanish means to carry out. A classic false friend.
darse cuenta
To realise, to notice something mentally — always darse cuenta de.
No me di cuenta de que era tarde.
I didn't realise it was late.
Always darse cuenta de + noun or que. Never 'realizar'.
¿Te das cuenta de lo que dices?
Do you realise what you're saying?
Often used as a rhetorical question to emphasise a point.
Me di cuenta al llegar a casa.
I realised when I got home.
The moment of realisation. Use preterite for the moment.
realizar
To carry out, perform or achieve — a task, study, plan or dream.
Realizaron un estudio sobre el sueño.
They carried out a study on sleep.
Formal register — realizar un estudio, un pago, una llamada.
Quiere realizar su sueño de viajar.
She wants to fulfil her dream of travelling.
Realizar un sueño = to achieve a dream. The nearest English meaning to 'realise'.
La reunión se realizará mañana.
The meeting will take place tomorrow.
Se realizará = will be held. Formal and administrative.
Tricky bit
'Realicé que...' as 'I realised that...' is a very common learner mistake. Say 'me di cuenta de que...'. Realizar is reserved for doing, not noticing.