This is a good thread. Thanks for starting it.
You can buy stocks through Computershare.com There are no brokerage fees or commissions. Pick a solid stock that pays dividends and park your money there. D.R.I.P. stocks build up. Dividend Re-Investment Program. The dividends go into your account, quarterly the dividends purchase stock and grow your stocks.
it's been ages since i've thought of DRIPs, and also about the actual stock certificates that you could hold instead of having them at a brokerage - when you bought or sold that meant those certificates needed to be sent through the mail and you sure didn't want to lose them. so in the end it just made more sense to leave things with the brokerage.
waxing nostalgic here a moment more for the older days when i was in an investment club and first learned about DRIPS and started doing them on my own too. before the computers were really going and the brokerage did not keep track of your basis in what you bought and sold so you had to keep track of that yourself. i am not doing DRIPS any more (explained below), but i did have a portfolio of about a half dozen stocks besides my regular ones (that were not set up to do DRIP).
i don't really miss that though now. computers can keep track of this and do the math when needed. so i'm happy for that. i do keep an eye on things. sometimes computers make assumptions that are not correct.
ok, so let's talk about basis, capital gains and losses.
as a beginning investor when you buy something the price you pay (plus any commission/fees) is the basis for that purchase. when you sell it, the price you get (minus commission/fees) is the net amount.
subtract your basis from the net amount and any positive amount is a profit called a capital gain (of which part may be needed to pay some taxes). if the amount is negative then that is a capital loss and there is no capital gain tax. some of the loss may be written off against income. note however, that all of this gets a bit fun when reading through the IRS publications or if you are doing complicated things and have a lot of other financial stuff going on you'll deal with your accountant or tax preparer.
back to DRIPS... (no it's not raining

)...
with a DRIP plan each reinvestment was an accounting event and i had to keep track of each of them. when i got to where i was starting to sell some things off i decided to simplify my life and accounting and sold the DRIP stocks off so that i was back to just my blocks of shares stocks that i'd been holding forever. gladly since then times have changed.

computers and brokerages are required now to keep track of things better.
now the brokerages will keep track of your gains and losses and basis automatically but you will be asked what accounting method you want to use for your stock sales. FIFO, LIFO or something else. FIFO is first in, first out, LIFO is last in, first out. etc. but all of this is important because you do need to know another thing about a stock purchase and sale. that is how long you've held it. because things you hold for the short term can be taxed differently than those you hold longer term.
all of this is described in the IRS publications. if you need something to read sometime...