After his return from Elba how did Napoleon expand the army? Did he issue edicts or whatever?
From Wikipedia: "Upon re-assumption of the throne, Napoleon found that Louis XVIII had left him with few resources. There were 56,000 soldiers, of which 46,000 were ready to campaign.[17] By the end of May the total armed forces available to Napoleon had reached 198,000"
How did Napoleon expand the army to 4 times its size in such a short time?
First off, that Wikipedia citation is a misreading of the original source, which is available for reading online. Charles Cornwallis Chesney's 1868 book does cite figures close to the "56,000" and "46,000" in that citation, but in a different context: "the real additions made to the army bequeathed by the fugitive Bourbon were just 53,000 to the total, and 43,000 to the real effective numbers, which stood on the 1st June at 198,000." What that's saying is that Napoleon managed to recruit 53,000 extra soldiers (43,000 effective soldiers) before beginning his Waterloo campaign. Not that he started with 53,000 (or 56,000 — not sure where that came from) and recruited an additional 140,000 men in a few weeks. So Napoleon expanded the army by 36%, not by 250%, per this source.
As for how he recruited troops? There was an attempt to expand conscription, including subjecting people to the draft who had previously been exempt — "mobilization now included married veterans and those under 1.57 m in height (roughly 5'2") who were formerly exempt," writes Peter McPhee (parentheses mine). But McPhee termed this "a desperate — and unrealized — mobilization." There were also attempts to mobilize militias, including tens of thousands in the "generally spontaneous" fédéré movement and expanding the age limits of the National Guard to "all able-bodied men between the ages of twenty and sixty" (Andrew Roberts, Napoleon: A Life). These had no effect on the Waterloo campaign, though. Instead, the real opportunity for Napoleon was re-mobilizing men who had only recently been dismissed by Louis XVIII. On Napoleon's abdication he left behind around 500,000 men under arms (some of whom were doubtlessly not available for action); to cut costs and satisfy international demands Louis dismissed nearly 300,000 soldiers and put many officers on forcible half-pay. Some of these veterans wanted to be done with war, but others did not, and it was from this crop of demobilized soldiers that he would draw on to fight the Allies.
Sources: