Please tell me how to make a small flower garden with proper drainage

What is your location and preference for plants

I start by marking my area- you can eyeball where you want your garden and what shape and size you'd like your finished patch of earth to be- for myseld I like to get my spade and a wheelbarrow and remove the top 6-8" dirt and lawn, others prefer to use string and stakes to create a template. Either way a porous substrate is placed at the bottom of your pit. You can use rock, sandy pebbles, mulch, sphagnum peat moss. Clean up the grass, seedling, weeds, and any non biodegradable refuse from your soil adding any ammendments to your soil before placing back into the desired garden bed. At this time you may want to place any rubber or plastic edging around the perimeter of you garden. Use the clean ammended soil to help keep the lining in place.

till the soil adding in garden soil, peat moss, some manure, and any other amendments you need. If it against the house, make sure the soil isn't below the level you need at the house, make sure the soil isn't hilled so that the water doesn't go to the house. Make sure you mulch your garden once you finish planting to help keep the moisture in the soil. If the garden is away from the house, prepare the soil the same way, but you can mound this one a bit for aesthetics. Put taller plants in the middle and go down in size from there when it is a free standing garden.

How to Improve Soil Drainage in Flower Beds | Home Guides | SF Gate

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Are you certain you need drainage? If you put the right plants for your growing zone in the proper location you should not have to incorporate special drainage.

If you place the proper plants for your growing zone in the proper location, you should not have to add in special drainage.