In opening a new account, the minimum investment can vary, usually ranging from $500-$1,000 (and even lower for IRA's and other retirement and education accounts). Most offer the option of either having an application form sent to you, or allowing you to fill them out online, print them, and mail them in with a check. The process is easy and can be done fairly quickly at almost all financial institutions.
Among the best discount brokers are E-Trade Financial, Ameritrade and TD Waterhouse. Each offers commissions of $8-$30 and have easy-to-navigate web sites. Almost all allow you to invest in mutual funds just as easily as in common stocks, which is a big plus for those who are just getting involved in managing their own finances. (Mutual funds are a collection of different stocks and bonds that are managed by professional money managers. For instance, if you wanted to invest in oil and / or gas and energy, but weren't sure which stocks in that industry to purchase, you could look for a mutual fund that dealt exclusively with those types of companies. You buy shares in the mutual fund, and the fund manager spends his time researching the different opportunities available.)
Once you have opened an account, you have the ability to start investing your money. All brokerages give you the option of setting up automatic monthly withdrawals, which will transfer an amount you specify each month from your savings or checking account to your brokerage account. This can be an easy way to start building up your equity; if you don't see it, you won't spend it. Since you won't notice the money that is missing each month, saving will be relatively painless.