You touch upon one of the major questions of doing history. A large part of a historian's education will involve questions like this, and many books and articles have been written on it. But that's not the only thing that makes it hard to give a short and comprehensive answer to your question. A complication in answering your question is that not all historians agree on what the answer to questions like yours should be. With that in mind, I'll try to give some largely uncontroversial and somewhat simplified pointers.

Firstly, you don't know everything. Even if we can be sure something did happen (and some historians/philosophers will argue we can't), we can never find out everything related to that event. If you ask how or why did it happen - there's always something to be added to that, some nuance to be added, some connection to be made, some archive to be explored. This is exacerbated by the fact that over time sources get lost or destroyed. In short: our knowledge is incomplete. We have to work around that (while keeping that in mind and taking that into account).

Secondly, you're working with interpretations. If an eyewitness recounts an event, they're giving an interpretation of their experience. If someone writes down their experiences in a diary or a logbook, they're giving an interpretation of events that happened. Some of these things will clearly be interpretations ("I believe one should always pay their taxes"), while others almost seem factual ("I paid 10 pieces of silver in tax" - Did they really pay tax? Or just say they did to seem to be a model citizen?).

There are two consequences following from the realisation that (almost) everything is an interpretation:

• You'll want to find as many different, independent sources on an event as you can get. If someone say they've paid 10 pieces of silver in tax, can that be corroborated in government records? Were there other witnesses?
• You'll want to find things as close to the original interpretation as you can. Imagine reading a book in which a researcher states that he found a letter in which someone states that he heard our subject say 10 pieces of silver were paid in tax. That's 3 interpretations where something might go wrong. So at a minimum you'd want to find that letter to read it for yourself to see if you agree with the third interpretation. That eliminates a chance to a possible falsehood (though plenty remain).

Thirdly, your own contribution is an interpretation. Realising this is half the battle. You can work to minimise the effect your interpretation has on your work. Examine your sources critically, especially those awesome sources which confirm everything you've ever thought. Make sure you can substantiate your claims. Try to distinguish between 'fact' and opinion. If you fill a gap in the sources with speculation, be aware you're speculating and might be wrong. Don't be afraid to say "I/we don't know". Use the phrase "According to X, ..." whenever there's a chance X might be wrong, or whenever X can't be corroborated.

These were some general remarks. I do want to touch on your specific question "Are [older history books] any more accurate than current ones since they are not as far removed from the time?". In general I'd answer "no" to that. Historians of say 150 years ago weren't as critical of their sources and they didn't really examine their methodology in the way we do today. Over the course of the last century this has gradually become better (a good reader will recognise this statement is an interpretation of mine). But this is when talking about history books. If you're talking about sources - letters, diaries, etc - (traditionally called primary sources), I'd say the closer to the event the better. It'll still need critical examination though!