Apply a pre-emergent herbicide, such as one that contains the active ingredient trifluralin, in the early spring before the weeds grow. It will not work after the weeds have germinated. Reapply per label instruction, typically every three months. A pre-emergent herbicide only works on some weeds, so check the label before using it.
Pull out the weeds by hand, getting all the roots in the process. Removing weeds when the soil is damp is easier.
Apply to the weeds a post-emergent weedkiller, such as sethoxydim, which is safe for irises. Kill broadleaf weeds with a nonselective herbicide such as glyphosate. Nonselective herbicides will kill irises as well. When using a nonselective product, paint it on the weeds rather than spraying. Read the herbicide instructions for safety, dilution and application procedures.
Dig up the entire iris bed if it is infected with a weedy rhizome, such as quack grass or thistle. Separate the iris rhizomes from the other weedy rhizomes. Throw out all the weeds and their roots. Dig down deeper, up to 6 inches, to get all the weedy root structures. If the iris rhizomes can not be separated from the rhizomes of the other weeds, discard them as well. When you are sure no weeds are left, replant healthy irises.
Install a border along the perimeter of the iris bed after eradicating the weeds. Plastic edging available in garden centers works well. Dig a trench and install the edging into the soil so only 1 to 2 inches are above ground and the rest is underground. This will prevent weeds that spread via roots from invading the iris bed underground.
Apply mulch in the garden bed to discourage weeds from growing. Apply 2 to 3 inches of mulch, such as shredded leaves or wood chips, around the irises. Replenish it as necessary.