I will be installing the laminate with the baseboard intact, do I lay the laminate right next to the baseboard? Or do I still need to use the spacers?
You should remove the baseboard, install the flooring, and then reinstall the baseboard. At least that's how I do it.
Most people leave the baseboard in place, and cover the expansion gap with quarter-round or shoe molding. If you're going to do it this way, you'll have to leave the manufacturer recommended expansion gap between the flooring and the baseboard. Than as I've said, you'll cover the gap with quarter-round or shoe molding.
First the manufacturer will tell you how much of a gap you need to leave. Read the instructions and follow them. Also for laminate your baseboards should practically sit on it. I would need to see pictures of what you are currently doing but we almost always remove the baseboards.
If you don't want to remove the baseboards then you will have to install some additional molding to cover the gap on your current baseboards. This is less work than taking off the baseboards but higher cost - materials and paint.
The preferred way to install flooring is to first remove the base molding, and then re-install it over the top of the finished floor. Any flooring material to a certain degree requires room for expansion and contraction. Installing the base molding over it would have the best chance of not having a noticeable gap in the flooring.
If removing the molding is not an option, the base molding can be undercut with an oscillating saw to allow the flooring to slide under it. Using a scrap piece of flooring, go around the perimeter of the room and mark the height of the flooring with a pencil. Then you can use an oscillating saw to carefully cut out the piece of baseboard. You may need to use a small pry bar to remove the piece.
You will most likely still need to install a piece of shoe molding after the floor is installed to completely cover the gap, but undercutting it will have a cleaner appearance than just butting the flooring material up to the baseboard.