Before we get further into the speak/talk/say/tell issue, let's take a brief look at the English word realise (or realize). Many Polish students assume it means the same thing and is used the same way as Polish realizować. Well ... it's not that simple. SOME meanings of realise are the same, but others are different. And the English and Polish versions are not always used in the same way.
First of all, the most common meaning of realise today is closest to Polish zdać sobie sprawę--that is, as the Concise Oxford English Dictionary puts it, to 'become fully aware of as a fact; understand clearly.'
I didn't realise that the door was locked until I'd spent five minutes trying to push it open.
Finally she realised that I didn't speak Polish.
Realise can also mean to 'cause to happen', to 'achieve', to 'fulfil', to 'give actual or physical form to (a concept or work)'. In these senses it is very similar to Polish realizować. However, in many cases when we want to express one of these meanings, we will use another word. For example, we don't generally realise things like research, experiments, or construction projects; we prefer terms like carry out, conduct, or complete. The verb implement is frequently used for things like policies or strategies, meaning to put something into practice.
Very often Polish will use a phrase like realizować inwestycję, where English would naturally say 'complete a (construction) project'. It's also important to understand that realise can also mean to 'convert (an asset) into cash'. In this case, if we were to translate the Polish phrase realizować inwestycję into English realise an investment, it could be read as meaning 'convert an investment (in, for example, stocks) into cash (by selling the stocks)'.
Once again, we're opening up a can of worms here; in the future, we also need to look at the words project and investment. But for now, the most important thing to remember is that most people, most of the time, use realise to mean zdać sobie sprawę.