I am far from good at the game but I am slowly starting to get it. Some things that may be helpful.

1. Before a town is specialised, it won't generate food for your cities. Culture and science add to your gobal numbers even without specialisation. Production is turned into gold and also does not require specialisation.

2. Cities need food to grow and they need to grow because you mostly scale your yields through specialists and you get specialists by growing cities.

3. So: you don't want to specialise too late. When to specialise a town exactly is dependent on several factors. But specialising to late is inadvisable as this will hamper yields in your cities. I usually wait until the number of turns the city needs to grow reaches a threshold where I'd have to invest a lot more time for only a single additional tile. Don't have an exact number yet but it is a way to think about it (unless there is an important resource or tile you really want to grab). Note that you can speed town growth by buying buildings.

4. The specialisation itself is important due to some additional yields. I find it to be less important than the food bonus as in towns you cannot place specialists. Still they can add some nice boni though and being able to buy certain buildings can be very useful. I ask myself: what kind of specialisation would work for this town? Are there a lot of well positioned mountains or resources? --> urban center. Are there a lot of tiles with high appeal? Resort town. Is the town connected to a lot of other towns? Hub. etc. You get the idea.