How to Bring Something Up...
The first few weeks of dating should be pretty drama free, especially if you're just spending time alone. You shouldn't be feeling too annoyed at him yet. This is the time he should be impressing you and making you feel great. No one is perfect so there may be times he will say or do things that will upset you. There is a time and place to bring this up to get the result you want.
Usually the first argument comes up when you're hanging out with his friends and you're feeling like maybe you're not getting enough attention or he's being a little flirty with a female friend. These hurt feelings are magnified after a few drinks. Guys typically bring you out early on in the relationship to see if you can get along with his crew. Most men find that very important in a relationship. If you feel the first flickers of anger, put your drink down and go get a water. Grab two glasses of water and bring one over to his friendliest friend. Talk to the friend for 15-20 minutes, or until you feel more calm. Ask for funny or embarrassing stories about your guy to help you feel less angry with him. Don't mention anything to the friend about being upset or annoyed because that information will just get relayed right back to your man.
If you still feel like you want to bring this up to him, wait until the two of you are alone either that night or the next day. Keep it short and to the point telling him you had so much fun with his friends but would love it if you were by his side a bit more since you are still getting to know everyone. Don't dwell on the conversation, keep it to a few minutes and he will be much more receptive to this information. Keep an eye on him the next few times you're out with his friends and see if his behavior changes at all or if he continues doing whatever it was that annoyed you last time. If the behavior does not change, maybe reconsider if this is someone you really want to date.
Another common first argument is lack of communication, especially after sleeping together. There is no magic day to sleep with your new guy to ensure everything will work out but there is a right moment. There has to be an emotional connection before you sleep together. Matthew Hussey has a really good story about this. He said the only time you can sleep with a guy on a first date is if you're hiking when suddenly you slip and fall and you're dangling from the side of a cliff. If he then reaches down and pulls you up to safety, you can sleep with him because you two shared an emotional experience. While let's not hope for something like that, wait until you see with his actions (not words!) that he is emotionally invested in you. Maybe he bought tickets to something a few weeks into the future or he has shared something really personal about his life, something that has made the two of you feel connected to each other. Of course he can always end up being a jerk but at this will give you a better chance weeding out the guys who just want to get laid.
Back to the lack of communication - what do you do if you want him to chat more? Rather than the boring "How is your week going? What are you up to this weekend? How's your day?", send a text that will make him smile and think positively of you. I don't typically recommend texting first but if you want to switch things up, you might have to set the tone. At the end of the day, he wants to date someone who has a full and complete life that has nothing to do with him. He wants to be with someone who is confident and secure. Sending an aggressive text, yelling at him that he hasn't texted you in a while, will not get you what you want. It'll probably scare him off or put a negative impression of you in his head. You could say something next time the two of you are together as long as it's very short and nice. Just something like, "You must be swamped at work! We used to chit chat a bit more. You think it'll slow down over there soon?" That subtly lets him know that you've noticed the cadence of texting has gone down.
Long story short, if you want to bring something up, do it in person and keep it very short and calm. Men respect directness but will shut down if the conversation seems never ending. If you really feel like you're not getting your needs met it might be worthwhile to really evaluate if this person can make you happy long term. The beginning is when they first see what they can get away with so it's important to not let bad behavior go on for an extended period of time.