The core of this task is to allocate funds according to the budget and to the priorities that your management has agreed on. If the budget and the priorities conflict, go to your manager for a decision.
You may need to put a system in place to authorize expenditure (e.g. a voucher or form of some kind) In any case, you will need to monitor expenditure and control against fraud and overspending.
Keep accurate, detailed records of resource allocation.
Schedule your reporting and your reconciliations