If you were to round up 100 genealogists, whether professional or amateur, and ask them one thing they wish they had known from day one, all one hundred would say "to source everything".
Everyone begins researching their ancestry for a different reason - for some it's seeing a photograph of our great-great-grandmother, for others it's being forced to for some junior highschool project. Most of us go into it having no idea that it's going to become a lifelong passion; it is for that reason that so few of us source things properly at first, and it is for that reason that we've all had to go back over our entire tree asking ourselves "where the #*@% did I get that information?" While that is admittedly a valuable learning experience, it's one you should nevertheless be spared.
The dead, it turns out, leave paper trails. Census records, marriage licenses, birth and death certificates, wills, newspaper mentions, and baptism records - just to name a few - are out there for most of our ancestors, it's just a matter of finding them. Finding them, however, can be a bit intimidating, as you will be convinced by your Google searches that you have to pay for this subscription or that record, and if you do not have the money to spare, it may seem that there's no hope of collecting these documents. Not true. Sites like Family Search and Find A Grave offer records, portraits, and burial information for free. You can download these images and use them as you see fit. Even Ancestry, which is largely a pay-to-use site, allows you to link records to your ancestors and relatives for free, if you have a tree with them. The catch is that you cannot download them unless you pay for a subscription (pro tip: if you cannot afford the yearly subscription, consider paying for a single month and saving as many records as you can over that time).
So, you've got a few tabs open, and you're ready to search for sources. Now what? One would hope it would be as simple as typing in your ancestor's name, and having all their records pop up. Ah, to hope. In truth, you have a lot to contend with. There were probably several people with your ancestor's name living in the same country at the same time. You may not know their date of birth or death, making it harder to narrow down which one is them. Census takers recorded names as they heard them, allowing for many mistakes. Searching for, and sourcing, our ancestors is not purely a matter of pulling up documents, it is just as much an exercise in deduction, in making intelligent guesses, in putting two and two together over and over again. For example, my 3x great-grandfather's name was Benjamin Ellis Trowbridge, and he was born around 1823. I have records, however, that list him as B.E. Trobridge born in 1828, Ben Trawbridge born in 1819, and Benjamin Troridge born in 1821. On the face of it, I cannot be sure that these are all the same person, but I do know that they were all married to a woman named Martha, they all lived in the same city, they all had the same occupation, and they all had a son named Sylvester. There's no such thing as an absolute guarantee in genealogy, but that's about as close as it gets.
In seeking sources for our ancestors, we must keep plenty in mind. Things then were not as they are today; I can tell you the exact minute my doctor recorded my birth (7:23 am, if you're curious) - my great-great-grandmother wasn't entirely positive of the year she was born (she favoured 1870, but she turns up on a census record from the late '60s). Not all that long ago, people were far less sure of what year they were born, what country their parents were born in, or their mother's maiden name. Oddly, we ancestral researchers end up knowing more details about their family than they ever did. We have the luxury of the library, the internet, and knowing that we should perhaps cast a wider net. We are able to look through numerous records and compile those most likely to match up to our relative. And that is exactly what we should be doing.
We also must be willing to reject sources - the very first John Smith you find on Ancestry.com is unlikely to be your John Smith. This is the biggest issue I see with people's family trees; they are so eager to grow their tree, they do not take the time to really read the documents they are attaching to their ancestors. They add anything they find that has the right name and the right general location, quickly accumulating dozens of "sources", turning their tree into a buffet of information. This, in turn, encourages new researchers to copy some of those "sources", which in turn makes things so much harder for those who want a truly accurate tree. Properly sourcing things takes time. You must be willing to read each document carefully, to do a little math, to seek out clues. And, you must be willing to set aside or outright reject documents that may bear your ancestor's name but no other resemblance.
TL;DR: The Quick and Dirty Version of the Above
1. Make it a priority to source everything: names, dates of birth and death, spouse, children, everything. Where you can find those things: census records, birth and death certificates, gravestones/cemetery records, baptism and christening records, obituaries, land deeds, local newspapers, just to name a few. Where you can find those things: Ancestry, MyHeritage, FamilySearch, FindAGrave, Newspapers.com, or, if you happen to live in the same region your ancestors did, your local archives.
2. Cast a wide net. Know that spelling and numbers may change slightly from document to document. If you cannot find any records for your ancestor using the information you've been given, go broader. If you think they were born in 1828, consider looking at 1827 and 1829 births as well. If their last name was Smith, consider that it may have been recorded as Smyth or Smythe.
3. ...but not so wide that it collects everything. Don't add sources just for the sake of adding them - be as certain as you can that the person named in the document really is your ancestor. Read each document carefully, looking for hints that it belongs to your ancestor: does their spouse's name seem right, and does it stay the same/similar from source to source? Is an address listed on the document? Do those addresses match up? If you find consistent facts from document to document, you can feel pretty confident they all belong to the same person. If you don't, you must be willing to discard them, or at least set them aside for further examination.
4. Be patient. Accurately sourcing each and every person in your tree will take time, and while that's not what anyone wants to hear when they're first starting out, I promise you it is a positive. The more time you take in researching your ancestors, the more you will learn about them, and the more you learn about them, the more you'll want to know. And that, that is what this is all about.