As someone very acquainted with Trotsky and his ideas, this is a good place for me to stop lurking...
Trotsky dealt with some fairly serious illness in 1924 and was disarmed politically in that year. So...you'd need to start by butterflying away the illness.
Stalin's base in the Communist Party was very strong in the "Lenin levy," the new members who came in after the revolution; Trotsky's was in the Red Army. For all practical purposes, you'd either need to break up the Stalin-Zinoviev-Kamenev troika or have Trotsky use the Red Army to coup Stalin. The former would've been hard to make work as Trotsky was extremely critical of Zinoviev, and wouldn't have looked to him as an ally, but Zinoviev's position as de facto leader of the Comintern gave him too much prestige to brush aside in 1924.
A Red Army coup would probably be the most realistic way of doing it, if Trotsky could claim that the Stalin-Zinoviev-Kamenev troika had basically done away with Soviet democracy (which hadn't really been operative since 1918 but who's counting?) or inner-party democracy. By 1926 Stalin had outmaneuvered the United Opposition, when Trotsky and Zinoviev finally did try to unite but to no avail.
The last attempt would be for Trotsky to use Lenin's Testament, but I'm not sure if it would've worked. It may have been a basis for using the Army to "enforce Lenin's last will" - but that's shaky and would probably lead to civil war or at least an early enactment of the purge fights (and not so one-sided).
Anyway, if Trotsky takes power - the national situation would've been very rough going. He would have had to "roll up" the New Economic Policy fairly early and institute collectivization of the farms; it would not likely have led to much by way of actual Soviet democracy. His international policy would have been one of support for foreign revolutions, possibly to the point when the USSR would for instance have supported the CP of China against the Guomindang in 1926/27 (Trotsky was a vociferous advocate of this) and the Comintern would have swung hard left in advance of the Depression. Assuming he could hold onto power, at the very least Trotsky's solution to the rise of Hitler to power was a socialist revolution in Germany, which would have meant he'd tell the KPD to start the revolution in January 1933 (if not earlier). Depending on how that went, you could see all kinds of butterflies - even if it was smashed, Trotsky would've been hardline in support of the Spanish revolutionaries, pushing for a revolutionary seizure of power right after Franco's rebellion. Likewise, he wanted the PCF to make a revolution in France in '36. His line of permanent revolution would've made Europe.... very interesting. A Trotsky wank of course would have one revolution lead to the next in succession, but you know.