By June, most of the spring-blooming bulbs have finished doing their thing. Remove the flower stalk when the bloom starts to fade, but resist the urge to cut back the dying foliage. The leaves need full exposure to sunlight to recharge the bulbs for next year. You can plant annuals or perennials in the gaps between the bulbs to conceal yellowing foliage.
June is also the month to pinch back your garden mums. Cutting new growth back by about half will stimulate branching and keep your plants more compact and produce more blooms. Repeat this process again in 4 weeks and then leave your mums alone to form buds for fall blooms.