A few factors will determine how soon you see or feel a difference.
Firstly, how long is it since you have regularly exercised, if at all?
Why are you exercising? Weight loss, muscle strenght and tone or general well being.
Do you tend to lose weight easily or do you struggle?
What exactly is your diet consisting of? Diet, I have always found is at least 60% of the battle.
How hard are you pushing yourself, are you swimming at a getle pace or are you really going for it?
Try to mointor your performance, either by time or distance and use this as a marker for continued improvement. As your fitness and cardio levels improve you should see a slight improvement in a month. If your aim is weight loss, dont weigh yourself daily, allow a good spell of exercise and good diet (2 weeks) this will give you a better indicator of how quick you are able to lose weight.
Remember diet is very important, more so than exercise if you want a visible difference. Load up an energy foods and slow release carbohydrates before training and then less carbs more protein for recovery after exercise. I always find it useful to allow myself a cheat day, where I eat whatever I want, at least 2-4 times a month and it does me no harm, in fact it gives me an insentive to diet!
Couple of further questions would be how old are you and how much do you currently weigh?
I am fairly up on the subject, although not officially qualified so I can give some ponters