Ear wax is naturally produced, meant to be there and should clear itself so that ear irrigation shouldn't be required (Ears are irrigated these days using a Propulse machine or similar, syringing is old school). Natural clearing of the wax may be problematic for those wearing hearing aids as they, obviously, occlude the ear canal.
The best solution is regular use of ear drops, olive oil or similar, to soften the wax and encourage it to drain. I would suggest putting drops in each ear once a week. Here's the important bit; you need to do it while lying on your side to let the drops soak down and stay on your side for a good 10-15 minutes, don't use cotton wool to try and keep the oil in place as it will just wick it out. Once the oil has soaked in turn your head the other way to let the oil and wax drain out and don't be in a rush to put your hearing aid back in.
Ear irrigation is one of my, varied, duties. It's not something I'm keen on doing. If the person has been instilling drops correctly it shouldn't need doing, if they haven't the wax is often still too hard to irrigate. It's a relativelty time consuming job, often requiring repeat visits and there is an inherent risk of causing damage to the ear drum. That said it is rewarding when big hard lumps of wax are coaxed out of the ear.