Runners should be removed except where needed as plant replacements. Strawberries do very well with drip irrigation, but any method where you can keep the soil moist is acceptable. Strawberry plants generally just need nitrogen which can be added in many forms ranging from ammonium sulfate to manure. The other plant nutrients generally occur in the soil in sufficient amounts. Mulch may be applied around the plants to keep weeds down and reduce fruit rot.
Organic mulches can can aggravate the pest problems.