“you must draw near.” This is the terminology for drawing close to the Tent of Meeting, where the ark (and thus God) was.
“tribes...family...household...man.” Israel was in Egypt for four generations (Josh. 7:1, 18; Gen. 15:16), and descending from Jacob there were first tribes, then families, then households, then individuals.
“Yahweh captures by lot.” The High Priest would use the Urim and Thummim in his breastplate to “take” or “reject” the thing in question (cp. Exod. 28:30; Lev. 8:8; Num. 27:21; Deut. 33:8). The word “capture” (cp. Fox, The Schocken Bible) is a strong word in Hebrew. Israel was to “capture” Ai after “capturing” Jericho (Josh. 8:19; 10:1; 11:12-16), but they could not because Achan stole the devoted thing and made the camp of Israel devoted to destruction. So now the Israelites must “capture,” by use of the Urim and Thummim in the High Priest’s breastplate, the one who was causing the problem, and they “captured” Achan and his family.