The most defining aspect of libertarianism is that the government should not get involved because the free market and/or local custom can provide better solutions. These noble-sounding ideals often hide something much more pernicious: paleoconservatism. Libertarians generally embrace federalism: a reading of the Constitution that grants the federal government only the powers explicitly listed (and then taking a rather narrow view—no Elastic Clause) and states' rights (harkening back to Dixie's attempt to secede from the Union over slavery and later Jim Crow laws). Paleoconservatism was the opposition to the expansion of the federal government under Franklin D. Roosevelt's New Deal: pro-business/anti-regulation, isolationist, states' rights, anti-tax, and often stridently racist and misogynist.
Paleoconservatives—and today's libertarians—prefer that more local institutions and customs dictate social behavior. Contemporary libertarians generally oppose racial and sexual discrimination by law, but many believe the social tool of ostracism is the appropriate way to further a socially conservative society (e.g., private business could refuse to patronize African Americans or gays; snubbing people of different ancestries would still be perfectly acceptable). Some libertarians are even okay with state or local laws enforcing a socially conservative outlook—as long as it's not done by "activist" judges or the federal government.
Libertarians generally believe government's role in business should be limited to enforcement of contracts through the courts and prosecution of fraud and crimes against the person or property only. Consumer protections go against this philosophy (caveat emptor—no "nanny state"). Environmental protections are also considered undesirable; the libertarian response to pollution and other environmental concerns is that, if people dislike it, they should vote with their dollars to buy another company's products or services; if this doesn't happen, economically, the consumer simply doesn't value environmental damage over the convenience/price of the product.
Libertarians generally accept the power imbalance between employee and employer: the feudal-like hierarchy of the traditional corporation, the authoritarian control of the employer over many aspects of the employee's life (sometimes even outside of working hours if that's part of the employment agreement). Libertarians generally believe, if you don't like the conditions at your current workplace, you own your labor, and you can take it somewhere else (where likely you may only find similar conditions in your current profession/trade). This is because libertarians see employment as a voluntary contract and the labor given and goods or services rendered as private capital, a fundamental good that should exist outside governmental purview. Libertarians generally accept the fact that this system will tend to create large imbalances of power and wealth and a stratification of the society (they may have a social-Darwinist retort for this). Libertarians generally don't see any problem with the disproportionate power for-profit corporations (after all, only voluntary associations of private persons) wield in our society because it's the private sector, not the public/government sector. The paradox that a laissez-faire economy will tend to concentrate wealth and power in just a few's hands doesn't bother or concern libertarians, most of whom believe they are on their way to the top, especially the Randian objectivists.
Libertarians are almost without exception scornful of the "welfare state": government-sponsored scholarships, government-backed student loans, disability income, unemployment income, job assistance, socialized health care, food stamps, Social Security, progressive income tax (preferring a "flat" income tax if there must be any income tax at all), and even public K-12 education in extreme cases. The nostrum is that the private sector can always do a better job; and for charity, churches, charities, and the philanthropy of private individuals is always a better idea than any systematic government involvement. This is in sharp contrast with the modern liberal and social democratic conceptions of the role of government.
When a libertarian speaks of freedom, they only mean freedom from a formal government's interference; their philosophy is unconcerned with how the contingencies of life—economic cycles, societal custom, imbalances of wealth and power—can and do have a great impact on most individuals' freedom to act according to their own principles and desires. This is in contrast with the liberal idea of freedom, which tends to promote equal opportunity, freedom of expression/speech, freedom of conscience/religion, etc. (i.e., liberals can see a role in government promoting individual freedom).