The Republic of Ireland international has been sidelined since suffering a hamstring injury against Manchester United at Villa Park on December 3.
Given, 35, had created a favourable impression after his summer move from Manchester City on a five-year deal.
But Given knows the performances of understudy Brad Guzan mean he can take nothing for granted ahead of Saturday's home clash with Everton.
Given said: "For me, it's been a frustrating time not to have been playing over the past few weeks. But I'm glad to be back out on the training pitch and I'm glad to be working to be match fit again.
"The hamstring feels great. I haven't had a hamstring problem in my life so it's a bit new to me, to be honest.
"I've recovered really well and had lots of good treatment and I don't feel anything now. I just need to sharpen up."
Guzan has been Villa's number two behind Brad Friedel and now Given but has impressed when handed his opportunity by manager Alex McLeish.
Given said: "I don't know what the manager's thoughts are, whether I will be in the squad to face Everton or not.
"I want to try and get back in as soon as I can and hopefully it will happen on Saturday.
"But every player has to fight for his place, however, and Brad has done a great job in my absence.
"I think you need competition for places in every position if you want to be a successful club and it's the same here with Brad.
"It does keep you on your toes, it does keep you sharp and working hard because you know you have a fight on your hands to try and play.
"That's the way it should be. You don't want it to be easy because you can take your foot off the gas a bit and it shouldn't be like that.
"The team have played really well also and I'm delighted for the team and I'm delighted for Brad because we've had some fantastic results over the past few weeks."
Given knows the difficulties of being number two after experiencing the same role himself at Manchester City behind Joe Hart last season.
He said: "This is the longest period of games that Brad has had since he's been here and he's done very well. I don't think he's put a foot wrong.
"Everything that has been asked of him, he's done really well and that's great credit to him.
"It's difficult to be a number two and to step up to the plate but he's done that. He hasn't looked at all out of place in the Premier League or in the FA Cup."