The 34-year-old could make his debut against Hearts on Sunday after finalising a deal following several weeks of training with the club.
Maybury had four years at Tynecastle from 2001 and quickly discovered the intensity of the capital rivalry as a first-minute goal from Ulises de la Cruz set Hibs on their way to a 2-1 win.
Maybury said: "I've not followed it closely recently but my second game for Hearts was a derby here and it really was a shock to the system.
"I came from reserve-team football in England and we were 1-0 down to De La Cruz's goal after 20 seconds and the place was rocking.
"But you quickly learn what it's all about. I have enjoyed them. The lads who have been in it will know what to expect."
Hearts have had more success in recent seasons, going 11 derbies unbeaten including the most recent and most important, their 5-1 Scottish Cup final victory.
Maybury, who could be joined by Gary Deegan in making his debut, said: "There are one or two like Deegan who will add a freshness, who just want to go out and play, which should help us too.
"It's a new era, they are trying to do things differently here and bring in players.
"The lads who were here from the cup final have spoken about their determination about making sure it doesn't happen again.
"I know how to approach it. You go out and enjoy it. you'll get the fans behind you because they want you to do well.
"There shouldn't be any extra pressure because of what has happened before. I've seen it from the other side that these results can carry you a long way.
"It's one to look forward to and enjoy it."
Maybury was released by St Johnstone at the end of last season and the financial uncertainty caused by the collapse of Rangers meant there was no certainty Hibs could afford to give him a contract until recently.
"I've been in training with Hibs all summer," the former Republic of Ireland international said. "I first got the opportunity to come in and train with no promises.
"Then things start shifting and players move on and they say they might be able to do something.
"Then I went on tour and played a few games and I was more hopeful.
"I was hoping we could have got it over the line before the start of the season but it wasn't possible. The way it works out, there is a possibility my first game could be the Edinburgh derby.
"If that's the case, I'll be looking forward to it.
"I'm sure I'll get a little bit of stick, but that's part and parcel of it.
"I played for Hearts a long time ago, I left a long time ago. But I don't think I never gave my all and that's what I've done at every club and what I'll do here.
"Nothing will change and if selected I'll give my all for Hibs."
