First, buying a house is a secondary goal. As any decent financial planner will tell you, establishing an emergency savings account the can provide 4 - 6 months of living expenses in case of emergency (hence the name) should be your first goal (set up a livable budget and stay within it). Once you have your emergency fund (which btw, will be more important once you buy a house) you start putting money away for your house. This delay also has the advance of proving you with a chance to build time on the job (lenders want you on the job for two years or some combination of higher education and job tenure that equates to 2 years - think one year on job and a bachelors). You also need to spend that time building your credit (easiest way - get a credit card, use it for purchases that are in your budget - for example food or gas - keep your high balance under 30% of your limit - if your limit is $1,000, do not go over $300 at any one time - and pay off the card every month when you receive the bill - not before and never late).
As for the house, there are a number of options once you can qualify (income, job tenure and credit history - see a lender about these). An FHA mortgage requires only a 3.5% down payment. On a $100,000 house that is about $3,500. A conventional loan can be gotten for 10% down ($10,000 down on that $100,000 house) and a regular conventional mortgage will require 20% down ($20,000). The first two mortgages will mean you have to pay Personal Mortgage Insurance which can add $100 - $200 to your payment. The 20% down avoids PMI bust is harder to save for. The upside is that a conventional mortgage with PMI provides you with the option to drop PMI once you hit that 20% in equity (you may have to pay for a new appraisal depending on how long between loan origination and hitting that 20%). FHA eliminated this option so if you can get to that 20% equity level, you have to refinance to get rid of PMI.
Last piece, the down payment is only one part of the equation. You will also have closing costs which can be about 5 - 6% of the purchase price - another $5,000 - $6,000 on our hypothetical house. IN all, plan on having at least $10,000 in the bank (based on that $100,000) before buying or $25,000 if you want to avoid PMI.
Note - many lenders also have home buying classes (obviously they will pitch their mortgages - shop around since 1.4 of an interest point can save you thousands). Take one - they are usually free and last about 3 -4 hours on a weekend morning.