There are 3 things that give a wig away. Lace, lumps and shine. The key to making a wig look natural is to minimize all 3 of them.
People's eyes go straight for the part on your wig so you want to make sure 1. It matches your skin tone and 2. It's not lifting. These are 2 dead give aways that you're wearing a wig. Get a pressed powder or foundation (even an eyeshadow) that's as close to your natural scalp as possible and press it on the part (or any exposed lace) to add to the illusion of your scalp. Soft lace tends to lift and roll more than hard lace which lays flatter because of the stiffer material. If you don't have sensitive skin (and don't care about your edges) go for a hard lace wig. For soft lace you could glue it down or Bobby pin the sides of your wig down. My favorite cheat is throwing a headband over the lace to conceal it completely.
Make sure your real hair is as flat as can be underneath. A lumpy part just screams wig. You want the wig to look like it's coming out of your scalp. Wig caps and head scarves can help to flatten your hair but ultimately it comes down to your choice of flat hairstyle. I recommend cornrows (stay in longer harder to take out) or flat twists (easy in but easy to come loose).
Our hair has a natural shine when it's healthy. Depending on what type of wig you have (human vs. Synthetic) depends on if shine’ll be a problem or not. Typically quality human wigs have a nice natural shine. Right out the box they might be shiny but a good wash should fix that. If not it's most likely poor quality or a synthetic wig, but it can still be fixed. Synthetic wigs are typically shiner because of its unnatural source. Lately wig companies are getting better at mimicking human hair wigs but if you get a ridiculously shiny, one dry shampoo and translucent powder are your friends. Apply till its a more natural shine. A good medium is to not look too greasy but not look like you're craving moisture.
Hope this helps!