In general, women in artwork in this time period wear veils and men wear skull caps or bare heads (so we can tell them apart). Here are observations of women in several paintings and carvings.
In the The New Minster Charter, 966 (source 1), the women in the lower left has long sleeves scrunched up; a shorter overdress on top of a visible long colored under dress; scrunching at the waist indicting some kind of lacing or belt (unclear); a veil; a cloak which overlaps itself in the front. The women in The Benedictional of St. Fthelwold, 970 (source 1) has a veil, a cloak, a long gown with a wide band of decoration at the bottom. The women in the center panel of Crucifixion Triptych (source 1) has a cloak with tasels at the corners. It appears to be rectangular. Many of the veils including the one in Junius MS. 11, Bodleian Library, pg 46 (source 1) appear to cover the shoulders as well as the head. The gowns seen in the Bury Psalter (source 1) are long but not particularly flaring.
Most of the veils in the above mentioned art are depicted as colored (blue, red, green The Missal of Robert of Jumihges, Mid 11th cent. (source 1)). I am unsure if the color was normal or added to religious art. Mary is frequently shown with a colored veil. The Missal of Robert also clearly shows that the veil is a long rectangle worn like a wrapped scarf. I believe this is called a head-rail.
The women in Crucifixion, Weingarten Gospels, 1050-1065. (source 1) are shown with the standard loose gowns of the 10th and 11th C but the elongated sleeve openings of the 12th C. A woman in the Detail from the Bayeux Tapestry also shows the loose gown with elongated (and trimmed) sleeves.
Overall, sleeves could be narrow and extra long (creating a scrunching effect at the wrist or in the later 11th C have the elongated opening seen in the 12th C. Gowns could be long (above toes) or short (knee length) on top of a long gown. Many gowns appear to be belted or laced at the waist, probably belted but the belt is not visible. It could also be back lacing which needs help to put on. Veils were common and frequently in the head-rail style. Wrapping cloaks that overlap themselves in the front were common.