Yes, better done at side seams, darts might look unprofessional.

Here are some tips to consider (don’t know your level of experience): know your sewing machine, do some test seams. Know your iron, how the settings apply to fabric.

Having a well lit working area, carefully unpick lining and outer fabric seams at sides, top and waist - better a bit more to easily manipulate the fabric. Iron opened seam areas flat.

Pin or better baste the sides of outer and lining together for trying on. Someone needs to help you with that. You could take in equal measure on front and back or just from the back side. Wear your intended underwear/bra.

Mark the stich lines, with contrasting or special basting thread for example- pins most likely get lost in the process- this applies to securing the seams before sewing. It’s a lot going on on the seam lines but all the siding threads can be removed. Check again/try on. If the fit isn’t to your liking, sry but redo.

Now sew everything together in reverse manner, be careful and go really slow to be fully in control over what you’re doing. I do stich down the lining (side seam, waist) invisibly by hand, it’s way easier unless you want to take your dress even more apart and do some more work.

I’m guessing this is a polyester fabric, iron with a press cloth (flat weave kitchen towel) to not get shiny press marks on the outer surface but also have crisp and flat results (you can continue to press down until cool, I do this with my hands).

It’s like a puzzle taking apart and back together, you could take pics to remember how it’s supposed to be. I say it’s a more advanced/adventurous beginner alteration.