Agence-France Presse has a handy guide to what happens next:
First, all parties embark on what are known as “exploratory talks”. In this initial phase, which has no time limit, there is nothing to stop the parties from all holding coalition talks in parallel - though tradition dictates that the biggest party invites smaller ones for discussions.
However, Armin Laschet, the chancellor candidate from Merkel’s centre-right CDU-CSU bloc, has said the conservatives would “do everything we can” to lead the next government, even after preliminary results put them a touch behind the centre-left Social Democrats (SPD).
SPD candidate Olaf Scholz, the country’s finance minister, also said voters wanted a change and for “the next chancellor to be called Olaf Scholz”. The Greens have called a party congress for 2 October during which they could decide with whom they would take up exploratory talks.
The pro-business FDP party, which like the Greens could play a kingmaker role, has said it has a preference for a coalition with the conservatives and the Greens, but a three-way alliance with the SPD and Greens remains on the table too.
On Monday, the parties will hold leadership meetings. The newly elected MPs from each party will also hold their first meetings next week, with the SPD and CDU-CSU planning to convene on Tuesday. The newly elected parliament must hold its inaugural session no later than 30 days after the election, on October 26.
If two or three parties agree in principle that they would like to form an alliance, they must then begin formal coalition negotiations, with various working groups meeting to thrash out policy issues.
At the end of these negotiations, the parties decide who will be in charge of which ministry and sign a coalition contract. This phase also has no time limit, with the outgoing government - Angela Merkel’s adminsitration - holding the fort in the meantime.
The parties then nominate who they would like to be chancellor before the official vote in the Bundestag.