There are 2 parts: Elimination and Communication. (Sounds simple enough, right?)
First, and most importantly, communication. How to tell when your little one is going to eliminate. Most kids grunt or squirm when they're about to poop and get suddenly quiet and calm when peeing. You can learn your own child's cues by letting him or her go diaper free, with a cloth diaper and no cover, or even with a disposable diaper that has a magic stripe on it like the pampers swaddlers sensitive. (As my husband says, "pee and yellow make blue.") Any way that you'll be able to tell immediately after your child has gone and you'll be able to start learning their cues. I also recommend that you take your child right after he or she wakes up from a nap. That's a common time kids usually go.
This is how you respond to their cues. I personally like to take my son or daughter to the toilet in the bathroom. Other people use bowls, sinks, bathtubs, a bush... whatever is convenient. Use what works for you and your comfort level. It's also common of ECers to use a verbal cue like "pssss" to indicate that it's a good time to pee or grunt to encourage pooping. This is useful if you want to cue your child to go in an unusual place like a new restroom or even their diaper. I don't see anything wrong with that, but I just ended up telling my kid that it's ok to go potty now and that seems to work fine.
Regardless of the receptacle, it's important to situate the baby in a way that makes him feel safe and secure. There are lots of ways to do this, but the bottom line is to just in a way that supports them as needed. For newborns, this means supporting their heads in addition to their bodies where a 6 month old wouldn't need that support.
Here's my daughter as a wee one.
You can see that she's propped on the toilet seat with a cloth diaper added for comfort. There's also I blanket on my knees for her and dad is helping support. All these are nice, but these luxuries aren't needed. (Nice that dad is there to hide her girl parts in the picture. I'm sure she'll kill me if her prom date were to ever see this in the future. Sorry, Elaine.)
Some more set up that works for us. I always sit on the edge of the tub to take off or put on the diaper. The diapers and wipes easily fit above the toilet. We can easily fit at lease a dozen disposables there but we could only fit 3 cloth there so we had to restock more when we used cloth and put a small trash can by the tub to toss used ones in. You can also see the lysol wipes hidden in the corner behind the toilet so we can easily disinfect if the aim wasn't completely successful. Oh, there's also a stool that my 2 year old now uses so she can hop up on her own.
Because of how we do the diaper changes, this eliminates the need for a changing table. In the first few months, we keep a mat out on the floor for quick changes but generally prefer to take my kids to the bathroom. It's more comfortable for me to change a baby on my lap than lean over the floor. Do what works for you and your family though. Oh, you'll also notice that I keep the baby angled toward the toilet... just in case.