Ask your airline when you book, or at least 48 hours before you fly. For Emirates: use Manage a booking on emirates.com or call Emirates. A travel agent can also arrange it. Tell them you travel alone, you are connecting in Dubai, and you want to be escorted to the next gate. Ask for a wheelchair or buggy for the whole connection and ask them to confirm it in writing. The airline passes your details to the airport assistance team.
On arrival, if you pre-booked help, Dubai Airports says to make yourself known to the dnata attendants at the arrival gate. If you cannot see them, ask the cabin crew or airport staff. On departure, help starts at the kerb in Terminal 3 or at the check-in counters in Terminals 1 and 2, and goes through to the boarding gate. Terminal 2 also has an Assisted Travel Lounge in the departures area. An exact meeting desk is not stated for each terminal.
Dubai Airports says assistance is free for people of determination, but it does not say how this applies to every older traveller, so ask your airline whether there is any charge. There is a wheelchair type with space for a bag under the seat, and standard chairs in three sizes. Emirates says there are priority lanes at connections security for people with disabilities. If you are not sure whether a lane is meant for you, ask a staff member before you join it. Call or chat with your airline if your plan changes.