These are internal US budget allocations, to spend money on US equipment and services for the intended benefit of another country (Ukraine). Money moves between accounts the same way as for any other US government expenditures.
The US DoD has a Foreign Military Sales program. It's basically a procurement office that operates between US defense contractors and foreign governments who pay for weaponry and equipment.
For military aid, the Foreign Military Financing program provides funds to be used through FMS as either loans or grants. The money itself never goes to the country receiving aid, it's more of a gift card for FMS. In FY2019, $115 million in FMF aid was budgeted for Ukraine.
The other big chunk of Ukraine money is through a separate initiative, the "Ukraine Security Assistance Initiative", created in 2016:
SEC. 9014. For the ‘‘Ukraine Security Assistance Initiative’’,
$250,000,000 is hereby appropriated, to remain available until September 30, 2016: Provided, That such funds shall be available
to the Secretary of Defense, in coordination with the Secretary
of State, to provide assistance, including training; equipment; lethal
weapons of a defensive nature; logistics support, supplies and services; sustainment; and intelligence support to the military and
national security forces of Ukraine, and for replacement of any
weapons or defensive articles provided to the Government of
Ukraine from the inventory of the United States
See also Public Law 114-92:
APPROPRIATE SECURITY ASSISTANCE AND INTELLIGENCE SUPPORT.—For purposes of subsection (a), appropriate security assistance and intelligence support includes the following:
(1) Real time or near real time actionable intelligence,
including by lease of such capabilities from United States
(2) Lethal assistance such as anti-armor weapon systems,
mortars, crew-served weapons and ammunition, grenade
launchers and ammunition, and small arms and ammunition.
(3) Counter-artillery radars, including medium-range and
long-range counter-artillery radars that can detect and locate
(4) Unmanned aerial tactical surveillance systems.
(5) Cyber capabilities.
(6) Counter-electronic warfare capabilities such as secure
communications equipment and other electronic protection systems.
(7) Other electronic warfare capabilities.
(8) Training required to maintain and employ systems and
capabilities described in paragraphs (1) through (7).
(9) Training for critical combat operations such as planning,
command and control, small unit tactics, counter-artillery tactics, logistics, countering improvised explosive devices, battlefield first aid, post-combat treatment, and medical evacuation.
So, again, this gives the DoD and State Department a fair amount of leeway to spend this money, including spending on support personnel, and on transfer of used US military equipment as well as new equipment. The initiative has been renewed each year.
The DoD is to inform Congress on the way this money is spent. I don't see anything in the law that would forbid transfer of some of this money as cash (for example, as part of intelligence operations), but that is certainly not the main intent.
These are just internal budget allocations, so the allocated amount is not necessarily spent as allocated (for example, it seems that only $223 million of the total $250 was spent in FY2016).