It sounds contradictory, but you can practice and improve your sight-reading skills. And, it's actually not that hard.
First, let's acknowledge that there is a hierarchy, an order of importance of skills. The top tier, the absolute most important level that we need to address first is the one that most people struggle with: notes and rhythms. But wait, that's two things - which is more important? They are equal; you must play the correct note at the correct time. Without both notes and rhythms in place, dynamics, tempo, articulation, and inflection have no context.
Since this is the tier of reading that most students have difficulty with, let's focus on it for a bit.
Notes - Most of us get most of the notes right most of the time. This is the half that we struggle with less. Even so, make sure you can actually name the note. It isn't "this one," it's a B. When you see a note that you're not sure of, find a note you do know and walk up or down the staff to find out the unfamiliar note's name. Now, notice something about that note that will help you remember it: it's below the staff, it has two ledger lines, and the note is below the second line, so it's a G. The more often you assign names to notes, the quicker you'll be able name the notes.
Playing scales and arpeggios will help your sight-reading in so many ways. You'll be more familiar with the notes on the staff, your fingers will be accustomed to walking up and down the instrument in steps and small intervals, you'll be used to the idea of reading different key signatures, and since our music is made up of scales and arpeggios (and they show up all over the place!), you'll find passages of moving notes surprisingly familiar when you play them the first time.
Rhythms - This is the half that trips us up most often. Sometimes it's because you find yourself struggling to keep the steady beat. A metronome can help, but you may also try this simple exercise: for the next couple of weeks, every time you are somewhere with music playing, find the steady beat and do something to physically match it. If you're in the car, tap your foot along with the song on the stereo. If you're walking with your iPod, try to match your steps to the beat in your headphones. If you're wandering through a store, tap your fingers with the music while you shop.
To master the skill of reading rhythm, the answer is quite simple: count! Actually speak the rhythms out loud. Lots of students skip this and try to intuit or "feel" their way through the rhythm. Many students don't even bother with that - they wait until someone else plays or sings the rhythm and then copy what they've heard. You'll be so much more confident in your reading and so much more independent if you learn to count for yourself, so take the time to sort out how to identify those eighth and half notes. Pay attention to when the notes are supposed to start and how long they should last.
When you're presented with a brand new piece, there is a process you can use to read more accurately. Take note of the key signature and time signature. Do a quick scan of the entire excerpt, and let your eyes find difficult passages, whether they look technically challenging or rhythmically complex (or both!). While your fingers follow along on the instrument, count in your head, keeping a calm and consistent steady beat. NOTE: No air through the instrument. Read and move fingers, but don't "whisper" through the instrument. You'll pay better attention to the reading if you are only reading.
Try not to spend too much time in one place - you only have limited time to take in an entire page. When you are asked to begin playing, you are aiming for consistency, not perfect accuracy. You will likely trip over a note here and there, but keep going! Don't try to stop and go back and fix and then go on, but try to maintain the flow of the piece. Sure, take note that, "oops that should have been an F#", but correct it the next time it comes around. Also, the first time you play a piece is not an occasion to go full-throttle. Keep the tempo at a calm and manageable pace, and keep your cool when mistakes are made.
As we've already discussed, notes and rhythms are your primary concern. Where you can add in ornaments (trills, grace notes, etc.), go ahead and do so; if you're unsure, leave them out. Check under the staff every now and then for dynamic markings - they'll be easier to implement than some other details because they are typically a broader marking than, say, articulations. As for slurs, staccatos, and accents, observe them where you can. Do not stop because of a missed articulation! There are lots of notes on the page - don't stop the train for a little staccato.
Remember, this is not a polished, practiced performance - it's a first reading done on the spot. Want to practice sight-reading? Pull out an etude book that you are unfamiliar with, and start reading. Go through the process on an etude. The biggest points of practice for most students will be resisting the urge to "whisper" while you read and continuing to play through mistakes. As with anything, it's going to be a bit of a struggle when you first get started, but keep at it. It will get better!