I am by no means an expert, but I can try to hit the major highlights as I understand them.
Just discussing taxable brokerage accounts... and assuming you're in the U.S.
First and foremost, you pay zero taxes on any dividends/cap gains if your taxable income bracket is 15% or less. So for 2017 (according to the chart I just googled) single filer upper limit is $37,950 and a married filing jointly is $75,900. As long as your total taxable income (which includes savings account interest, working income, dividend/cap gains, unemployment...etc.) falls under those limits (depending on your single/married status), you won't pay anything towards taxable account moves. And if you're really near the income cut offs and a distribution or cap gain pushes you up into a higher bracket, at least you'll only pay tax on the amount over those limits, so it's not like it will be a terribly costly amount owed.
Reinvestments just mean you're creating new tax lots of the fund however often it reinvests. So if you do decide to sell, checking to make sure the amount you want to sell off includes only long term (over 1 year's time) of funds is a good idea. I have my taxable account set to not reinvest automatically because I use the cash for living expenses (and it counts towards my taxable income anyway so might as well use it). But if you are still building your investments, it is generally a good idea to reinvest automatically. Fortunately, most companies now automatically track the funds' investment dates and cost basis for you so you can see pretty easily what amount of funds is in the long term and short term.
If you don't sell off anything, then you don't realize capital gains. BUT some funds do distribute dividends (twice a year seems to be average - small distribution in spring and larger one in December) so be aware of funds doing this and either minimize holding funds that do so, or make sure to figure into your taxable income. Avoid buying funds right before a distribution because you're going to be assessed that distribution and may owe taxes on it (which would suck if you JUST bought a bunch).
Short term capital gains are taxed higher than long term cap gains. Hold a fund at least one year before selling it, and it becomes a long term. Simple way to avoid a higher tax hit.
Good place to start:
https://www.bogleheads.org/wiki/Tax_basicshttps://www.bogleheads.org/wiki/Capital_gains_distributionhttps://www.bogleheads.org/wiki/Dividend