EVEN if you have a truly tiny garden you can still grow alpines in a trough or other shallow container. If possible, situate it near the house where you can easily keep an eye on it, allowing you to monitor it for pests or other trouble, but also to sneak out and watch new flower buds unfolding.
Make sure that there is a drainage hole in the bottom ("drainage, drainage, drainage" is the mantra of alpine gardening). Prevent this from getting blocked by protecting it with broken shards of flower pots or similar material. Add a few centimetres of grit or gravel and put in your compost mix. A couple of trowels of well-rotted manure in the bottom layer of compost will give the plants a reserve of food as they grow.
If you have room, "plant" a few well-shaped rocks to make a miniature landscape (be sure to align them in a natural-looking way) and put in the plants. Water in gently and dress with grit.