After playing over thousands of Blackmar-Diemer Gambits I sat down one day to see if I could summarize the more usual development of White's pieces. Tim Sawyer liked the result well enough to ask permission to use it at the beginning of his second edition of his Keybook.
The BDG is a classic gambit, in which white trades material for a compensating advantage in time and space, and seeks to capitalize on that advantage with a direct attack on the enemy king. White obtains quick development, open lines, and active pieces. Black must defend carefully, but strike a prudent balance between aggression and passivity, seeking to gradually equalize in time and space, when his material advantage may become telling.
Pawns: The pawn structure provides white half-open e and f-files as avenues for pressure from his rooks. On the negative side, white's d-pawn is weak on a file that is half-open to black, whose counterplay often involves an assault on this pawn with c5.
Knights: White's knights are classically developed to c3 and f3, the latter with the capture of the black pawn that is the distinguishing move of the gambit. From f3 this knight often reaches e5, striking deep into black territory, while simultaneously opening the f-file for white's rook after white has castled kingside. The knight on c3 often participates via e4 on attacks on black's f6-square, often the Achilles heel of the black position. In more positional games it may be required to retreat to e2 to hold d4 and allow c3 to further reinforce that square.
Bishops: The development of white's bishops best awaits the determination of black's pawn structure, further confirmation of one of the axioms of chess, "knights before bishops." When black fianchettoes his bishop to g7 white's B/f1 usually goes to c4, bearing on the f7 square, while in most other lines the bishop is better placed at d3. From there it often has the opportunity for classic sacs on the h7-pawn. Where to place white's B/c1 is not as clear. Often it pins the black knight at f6 and increases the pressure on that square. Sometimes it goes to f4 to help control e5 and threaten tricks with the N/c3 against black's queenside, but it has the disadvantage there of at least temporarily blocking the f-file to white's rook. Finally this bishop is developed to e3 in some lines to help hold the d-pawn--a task I personally find distasteful.
Rooks: Since white's rooks come into play later in the game, their development is even more dependent on the course of the game to that point. However, they are often doubled on the f-file, bringing tremendous pressure against the key f6-square. The R/a1 also often goes to the half-open e-file or to d1 to support the white d-pawn, or in anticipation of that half-open file soon being fully opened.
Queen: The white queen frequently joins in a kingside attack from h4, reaching there via e1, or taking an extra tempo, by way of d2 and f4. In some cases the queen may go to d2 to support a bishop on g5 and later trade off a black bishop at g7. In other cases the queen may need to go to e2.
King: Finally, the white king usually castles kingside. This allows it to reach safety at the earliest possible opportunity while at the same time bringing the R/h1 to the half-open f-file. In more positional BDGs the king sometimes castles long, but usually the extra time this takes does not seem to square with the essential concepts of the gambit.