Unfortunately, the first thing you'd need to do would be to find a way of travelling back in time. A substantial number of episodes no longer exist (as far as anyone knows). See Missing episode for an explanation of why episodes are missing & for a list of the missing episodes.
For the surviving episodes, watching the DVDs is likely to be the best approach. See List of BBC DVD releases for those available. Bear in mind that episodes quite often appear on more than one release, so you can see all the available episodes without having to get hold of all the available DVDs.
All lost episodes still exist in audio form. BBC Audio and its successor, AudioGo, released box sets of these episodes (now out of print after AudioGo went out of business in 2013). So it is possible to experience every existing Doctor Who episode, if you don't mind just listening to some (the audio releases include narration to explain visual action). It is also possible to experience missing stories through the novelisations published by Target Books, though these do not already completely reflect what was broadcast.
Missing episodes are sometimes recovered. For example, the missing episodes of "The Enemy of the World" were recovered in October 2013 & released on DVD in November of that year (2 days after the 50th anniversary of the show). Recovery is an unpredictable process -- there's no way of telling what will be found, or where, or when. As of summer 2014 the only recovered episode that has yet to be released on DVD is an episode of "The Underwater Menace".