Since [@shylarah] brought up some of the other points I would've mentioned if I had gone further into it earlier, I might as well make another post instead of edit the previous one like I said I might. They did a good job bringing up some of the elements that I mentioned when I said certain type of psychological conditions might cause it to have no effect at all, or a reverse effect. Since the original poster seemed to be planning on writing from the context of them actually feeling guilt, I tried to focus on those aspects of the experience.

Certain types of psychological conditions, such as if the character is a psychopath, would have an impact on how they experience the act. These types of people usually lack the capacity for any sort of concept of morality or genuine feeling towards others. They are fundamentally self-centred people who view the world in a very superficial way, though they are often very good at pretending to be capable of the depths they completely lack. They never understand the feelings of other people on anything more than an intellectual level (they understand the words but not the soul) and lack empathy, and usually always view the worth of others based on whether or not those people are useful to them. Many of them are able to commit murders or torture others with the same level of ease and apathy that they would experience from mundane activities like brushing their teeth.

While some people will exhibit this sort of detached behaviour to the experience of killing another as a defence mechanism to deal with the shock and guilt, people like this will openly feel nothing about what they did, or may even just rationalize it as "kill or be killed", "survival of the fittest", or some other way of trying to use logic to detach themselves from the more emotional and moral elements of what happened. This sort of mind state where they fail to acknowledge the act of killing as important is definitely the sort of mentality that a large amount of military training brainwashes into people, or those who become contract killers, and it's not entirely common for people to merely look at the lives of others as numbers or statistics for some scientific experiment or self-serving materialistic agenda.

As they mentioned in the previous post, mentality's involving misanthropy, becoming jaded or cynical or pessimistic, or, as I'll now add, nihilistic ideologies and Machiavellian perspectives of the world, will result in a similar type of total indifference towards the events of taking another person's life, and in some of their cases they may even come to enjoy it. In some other people's cases, they will so often that they actually get used to it, again resulting in apathy and nonchalance about their acts. Since you seem to be writing from the perspective or someone who has done it for the first time though, this is probably not what you had in mind.

People who come to hate other humans, or who exhibit qualities that have been mentioned by me and the previous poster will also, as stated, have the possibility to create a person who actually enjoys killing others, and certain types of other personality traits such as being a sadist can have the same sort of effect. A lot of people also kill out of lust, but, I noted, the topic is based on the idea that the person is more conventional in their reaction to death and is also doing it for the first time, so some of these answers aren't what you want. People could become consumed by bloodlust or excitement about the events for a number of reasons, so it's not, as they said, impossible that they will experience it positively. They could also not care, as the previous poster said, for a variety of reasons other than those I mentioned.

It's not pretty, but it's nature. This likely isn't what you have in mind though.