Played ASLSK scenario 1, Retaking Vierville. Set on D-Day+1, the American paratroopers have secured the town and moved on leaving a token defence. The Germans decide to try and sneak back in. The Germans win if they can control at least one of the four victory buildings in the centre of the map.
Not having played this game before, it took us about a turn and a half to get used to the different firing options for our troops - and there are many of these. It's all about laying down covering fire/base of fire with some fire groups, while you advance other units in under that fire. If you've thought it out and the dice run your way, you should make progress.
My German opponent moved onto the map on the first turn but didn't take advantage of the four US squads out in the open in town. They quickly fled into the buildings and maintained a defensive position to hold on while reinforcements arrived. As more units from both sides moved onto the map board, the US troops where basically boxed in on three sides and the battle reduced to a city firefight with the Americans getting the best of it. This was due to some large fire-groups being set up on turns 3-5, and some truly appalling die rolling by the Germans. A German concession at the end of turn 4.
This is an ideal starting scenario as there is low counter density and more units trickle onto the map, allowing you to grow into system and develop your options. We had a good time and are keen to try again - I guess that's the whole point of the starter kit.
I recommend downloading the Starter Kit sequence of play cheat sheet that somebody developed. There are links to it currently on Consimworld in the Boardgaming - WWII Game Series - ASL folder, around May 5th.