Weeding is the most tedious of all the maintenance jobs and prevention is so much easier than cure. Begin at construction time. Make sure that the planting site is free from all perennial weeds and that weed roots are absent from the topsoil used for making the planting mixture.
It is unfortunate that however careful you are at the construction stage, weeds will still appear and they must be tackled promptly as dwarf plants such as alpines can be easily swamped by them. There are a number of sources of these weeds and you can cut down the work of weeding if you take preventive measures. Firstly weeds are often brought in with the plants, always check carefully and pull out stem and roots of any weeds which are growing on the soil surface of the pot.
Next, perennials can creep in from surrounding land, create some form of weed-proof barrier if this is likely. Finally weed seeds are blown on to the site, remember that this includes the seed from nearby rock garden plants which readily produce self-sown seedlings. Deadheading and weed control in surrounding land will reduce this problem.
Hoeing is not practical but pulling out the weeds by hand is the usual method to tackle the problem. You may need a narrow trowel if the roots are firmly anchored. Of course not all self-sown alpines are 'weeds'. You will only need to pull out seedlings which are growing where they are not wanted. Perennial weeds are a difficult problem when the roots are too deep and widespread to be removed. The answer here is to paint the leaves very carefully with glyphosate. Never spray weedkillers and never use lawn-type ones.
During the first few weeks after planting you should water regularly even if the weather is not particularly dry. Once a plant is established it will only need watering during prolonged dry weather. A plant should never be left to show visible signs of distress during a period of drought. The time to water is when the soil at a few inches depth is dry and the foliage looks unusually dull. Once you decide to water then do it thoroughly. A light sprinkling will do more harm than good. Apply two to four gallons per square yard, a hose is much better than a watering can unless your rockery is a very small one. Do water carefully and slowly so that the plants are not dislodged and repeat the watering as required.
As this is my first year with a rockery I made certain the plants were well watered, sometimes twice a day. The wonderful advantage of using your hose with an adjustable sprayer is that you can water certain plants thoroughly and other plants can be sprayed sparingly. The watering can is probably the best method in the beginning as the plants are very fragile and a light sprinkle accomplishes the task without spraying soil out of the rock garden. Don't use your sprinkler the first year, I tried this method and the result proved horrendous. I monitored the site about twenty minutes later. The area was too wet, the soil had moved to the drive and sidewalk and a few plants had to be repositioned. Watering is so vital and the appropriate amount must be maintained to keep your rockery looking splendid every single day. Please use extreme caution and never let the plants dry out as wilted, brown specimens ruin the overall appearance.