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I have a Canon 60D that I use for my primary hobby that is photography, but sometimes the pictures that I took are with the incorrect exposure like this:
So I want to know how I can choose the correct exposure for situations like night, intense light, poor light conditions...
PS: The image is intentionally unfocused because I was playing with styling my photos a bit, not that it's a problem.
There isn't really any "correct exposure". You can expose a picture however you like. Some choices may be more typical, and if you expose photos in a moderate, even way, it will tend to appeal to most people without a thought as to the exposure as an element of the composition. In other cases, you may choose to make the exposure darker or lighter, perhaps making the photograph low key or high key. If this is very strong, it will become a central element of the image; if it's more subtle, the effect may just be subconscious. Or, it may cause some viewers to dislike your choice, which is okay, because hey, it's your photo.
In most compositions, choosing how bright to make the main subject is the most important point. If that's all you care about, and you just want to make it medium brightness, spot metering might do the trick. Usually matrix or evaluative metering will too, with more consideration to the rest of the frame as well. (See When best to use Multi-Zone/Matrix, Spot, or Center-Weight? for more on metering.) Relying on the camera's metering will give you an average-brightness exposure, and you can use EV compensation if you decide you want the image to be brighter or darker than that.
The dynamic range of the whole scene you are photographing is an important thing to think about too. If there's very dark areas, keeping the exposure low will lose detail there; if there's very bright areas, a higher exposure will cause blown highlights. In many common cases, there's enough of both that you can't satisfy both sides given the technical limitations of cameras, so you need to make a decision as to where you will compromise. It's possible to use techniques to compress the range into one image (for example, "HDR"), but that can look unnatural. So, usually, choosing where to keep detail and where it's okay for detail to be lost in shadow or "blown-out" into white is a crucial decision.
In general, a thought process for exposure might be:
and the exposure choice follows from there. Many people find that Ansel Adam's Zone System provides a good framework for this, even in the modern digital age.
And really, I don't feel like my answer here is complete without a plug for a book by one of my favorite authors on photography, Michael Freeman's Perfect Exposure. This book goes beyond the typical what-is-metering, what is aperture, etc. questions (which, by the way, we cover pretty well here under camera-basics), and looks carefully at a photographer's mental process for choosing the "correct" exposure for a given photograph to meet a certain intent, with both practical examples and theory.
I'm guessing that we're going to run afoul of the term "correct" here, because you're trying to take a nighttime scene and make it appear as if it's daytime, which isn't really a faithful reproduction of ambient conditions.
Artistically, you're absolutely free to do exactly what you're describing, and in some cases, this can turn out really well. Soft, even light (diffused moonlight, maybe) across a scene could work really well for this, I believe.
In order to increase exposure, you could use exposure compensation (probably available in several of your camera's modes), but to really turn night into day, you're probably going to have to go into manual mode and set up a really long exposure. Make sure you're tripod-mounting your camera in order to do this, and slow the shutter speed until you get the effect you're looking for.
In a shot like your example, though, where lighting isn't really diffused at all, but rather, is coming from all those point sources on the horizon, I believe you're going to blow out all those highlights before you really achieve anything that looks like daylight.
I am going to give a general answer and propose a modified form of the Zone System which I call the Highlight Zone System. Its goal is to preserve selected highlights faithfully. It is also known as 'expose for the highlights and develop for the shadows'.
The principle is that for most, but not all, subjects, faithful reproduction of the highlights is what matters most. In post processing you can adjust dark or mid tones to your taste and the limits imposed by noise.
The human eye selects the brightest point in its view and treats it as pure white. Of course, there are limitations to this. If the brightest point in the eyes' view is very dim or is not even close to white, this effect no longer applies.
All other colors are referenced to the brightest point.
The illustration of dynamic range on my camera, below, illustrates why this matters.
The sensor has a sharp cut off as brightness approaches saturation of the sensor. Thus it is easy to burn out highlights. So we have to expose carefully for the highlights to avoid burning them out and losing detail.
References
Zone System - Wikipedia
A Simplified Zone System for Making Good Exposures - Norman Koren
White Point - Ron Bigelow
Modern exposure technique, at least outside a high-pressure professional environment, is basically about quick feedback and exposure compensation. That is, let the camera decide, then look at the screen (with the histograms on) and dial in some compensation.
When you've done this for a lot, you start getting a feel for what's happening and develop an awareness for what the camera will do and how you will compensate even before you shoot.
One thing that could help in developing this awareness is to switch off matrix-metering and use a plain center-weighted pattern.
