Bush was pulling out of Afghanistan. Obama criticized him for it, and said we needed to pull out of Iraq and go into Afghanistan. Which he has done.
The first troops sent to Afghanistan under Obama was in the spring of 09 but had been set up by Bush and was under Bush's budget.
Obama's first decision on Afghanistan would come in Oct 2009 and he had begun to publicly express doubts because the spring deployment had been largely unsuccessful.
That is when Dick Cheney made his famous statement about Obama "dithering on Afghanistan".
Cheney said Bush made a policy change on Afghanistan, let candidate Obama have a look at it and Obama adopted it as his own, but was now dithering.
That was a major media event and a Google search of "Obama dithering on Afghanistan" will get many results.
Eventually Obama did give the order for more deployments to Afghanistan and eventually put Gens Petraeus and Allen plus ambassador Ryan Crocker in charge of Afghanistan. These were the same 3 men that Bush put in charge of Iraq in 2007.