To make authentic looking spaghetti you will require a julienne peeler. 

Method 

Run the peeler down the full length of the courgette. Repeat on the same side making long pieces of courgette until you reach the seeds in the centre. Make a quarter turn in the courgette and begin again. Go all round the courgette until you have an oblong strip of seeds which can be discarded. Be careful as you near the end of the courgette as the julienne peeler is sharp and you could easily cut your finger. 

Heat 1 teaspoon of olive oil in a frying pan on a high heat. Try using a flavoured oil such as garlic or chilli oil. When the oil is hot, toss in the courgette and stir. Fry for 2-3 minutes, stirring regularly. When cooked the courgette should be soft with a few burnt edges. Season well with salt and pepper before serving. 

Serving Suggestions 
Serve with a Ratatouille or a Bolognese Sauce, flavours such as garlic and tomato work really well with the courgette, although feel free to try out your own favourites. To make the meal more substantial, chicken, fish or prawns work really well too.