Brecourt does not resemble any map from the singleplayer game. Based on the Brecourt Manor Assault by members of Easy Company of the 101st Airborne on D-Day, the map is essentially a large, open meadow with a system of trenches, two small walled areas on opposite sides, and a thick hedge running through the middle. The trenches join several large 105mm guns which were the paratroopers' original targets, however they are inoperable here. It's a sniper's dream map, and even novice snipers can practice their skills here. Brecourt is popular for Capture the Flag but is not played much in other modes.
Like stated above, Brecourt is played almost exclusively in CTF. But if you do find yourself playing TDM or DM, the best strategy is to grab a sniper rifle and creep across the map, picking enemies off.
The American flag is located by the shed, within the low-walled area; Germans should try to hug the hedge for most of the way, then have a few players (preferably with MP40s) rush in for the grab while others pick off defenders. Retreat along the trenches for the trip back. The German flag is in a more open area, on the opposite side of the map, so the defenders are more likely to be sniping from the nearby walled area rather than physically near the flag. Jump up from the trenches and get the flag, then run like heck, taking a right into the trench that leads you into the other side of the hedges. From there, concentrate on not becoming a target for snipers.
The two machine guns in the trench on the American side of the map can be used for defense, but keep in mind that Germans can secure that area and turn one of the guns against you. It's not advisable to use those anyway, since you'll become a really easy sniping target. Enemies from the direction that the gun is facing can obviously get you, but frighteningly for American players, the German spawn area (the walled one) has a few spots where they can scope in and shoot you straight through the long trench.