First and foremost - lolita is an expensive hobby, in the sense of both time and money. Cheap clothing with no time or thought put into it isn't lolita. Lolita is defined by it's elegance, and elegance doesn't come easy and it doesn't come cheap. But it easy possibly to afford it through several different means.
♥Save up for it. It cold take a week or it could take a year, but it can be really worth it.
♥Learn to sew.
♥Spend lots of times hunting for sales, second-hand bargains, and lucky packs.
♥Convince a friend/parent/spouse/significant other/family pet to buy it for you.
Some of these methods are obviously more effective than others. Anyway, onto the basics you'll need to begin your wardrobe. You don't have to go in this exact order but sometimes it's helpful to have at least one each of the first few items when starting out.
Additionally, some really great advice on building a wardrobe on a budget can be found here.
This piece will be most easily recognizable as lolita even when mixed with your usual clothes. Select something in a color and style you love with but make sure you can coordinate it with stuff you already own or things you plan to buy soon. Look for skirts with nice bell-shapes - though circle skirts are coming in to fashion more and more, and MM and VM have put out a few fitted skirts. These are good pieces to start with because they are lolita by themselves (even when worn with tshirts) and will set the color-scheme for your outfit.
You'll need this to get the maximum floof out of your skirt. A white petticoat will probably be of the most use since it won't show through lighter fabrics, but if you plan to wear mostly black skirts a black petticoat might look better. Try and invest in a well-constructed petticoat because it will be the foundation of your lolita outfits. If you haven't quite gotten around to purchasing a petticoat, layering other (shorter) skirts underneath the skirt you want to wear is alright for a temporary substitute. You may also want to get some bloomers if you need some extra foof or plan on being very active.
A nice solid pair of black or white Mary Janes will go with almost everything. Avoid colored shoes unless you plan to build an entire wardrobe on that exact shade.
A great guide to buying shoes can be found here.
A good blouse is essential to your lolita wardrobe so look for one that goes with everything. Your best bet is a blouse in white, slightly off-white (if the lace on your other clothing is off-white), or black without too much going on (no weird bows all over the place or anything like that). If you can find one with detachable sleeves that's even better, because it'll work in all weather. Look for a blouse that's nicely fitted and that can either be worn alone or with other clothing on top (so nothing too poofy) and one that's comfortable enough to wear frequently.
Any hair accessory is fine (see Anatomy of a Lolita Outfit) so long as it coordinates with your dress or skirt. But if you're new to lolita it might be best to start off with a bow or mini-clips rather than plunging headfirst into frilly headdresses and bonnets. These items are non-essential but are great for creating the perfect coordinate.
Another technically non-essential that still really contributes to the overall loliness ^_^;;; Again go for a pair in white and black that'll go with the blouse you've choosen and future clothing, though if you really like a colored pair that coordinates with the dress or skirt you bought go ahead and go for it if you plan to buy more things in that color. Again a way to ease into this is with simple socks, without all the lace, but it's entirely up to you.
So you don't end up like me carrying around a beat up Chococat purse in your lolita finest find a nice bag that goes with all the other things you've purchased. If you like having lots of different purses go ahead and buy one that coordinates with your skirt and dress, otherwise go for a simple white or black purse that doesn't have too much going on (avoid trim and appliques that might clash with other outfits).
The perfect way to keep warm and be lolified all at the same time. While you can only wear your new lolita skirt a few times a month, a coat can be worn almost daily (provided you wash it :P). And even the frilliest of lolita coats still looks awesome over your other clothes. For long coats any color is fine since it covers the clothes underneath (so it doesn't matter if it coordinates), but for jackets try and coordinate it with your skirt or dress (e.g. don't buy a pink jacket to wear with a bright blue skirt).
Once you have the basic items you can start adding things like jewelry and parasols now that you know what you need to coordinate it with. It's much easier to coordinate jewelry and other accessories to your dress than it is to find a dress to match pre-bought accessories.