There are a lot of things involved in sightreading rhythms -- things that make it difficult. The traditional "counting" method helps with some of these, but it is a significant distraction (since you have to count in addition to everything else you're doing) and it doesn't help much with two of the most fundamental skills sightreading depends on:
The Rhythm Card method develops the time sense by using the musician's body as a metronome. Walking is a natural, automatic action which can be done without thinking, but it's impossible not to notice when something that's supposed to be in sync with your walking gets out of sync. Because this feedback is immediate and unambiguous, reliable correction leads to steady progress.
The Rhythm Card method develops the musician's mental buffer by removing the notation from view during the period it is performed, forcing the musician to remember what was previously seen.
And, because walking and moving cards from hand to hand can be done easily and automatically, the musician's complete attention can be directed at interpreting the rhythms.
The basic idea is this: you have cards with rhythms written on them. Each card corresponds to the same amount of time -- say, two quarter notes. You walk, and as you walk, you deal the cards from hand to hand, moving one card each time your (say) left foot hits the ground. This pattern sets up your body as a kind of metronome. Each time a card leaves the "from" hand, you begin to speak/sing the rhythm. Because you can't see the card once it's been moved, you develop your rhythmic memory.
Beyond the basics are many variations, depending on what skill level you're at, what you're trying to learn, and what you run into.
First, the cards. How big are your hands? Unless they are unusually small, I recommend you use double-sided-blank playing cards. These are smooth and slide across each other without much resistance. If you live in a very big city (like NY, LA ... ) you should be able to find these in a magic shop. If you run into trouble, let me know.
Besides the cards, you need something that writes on them; they're slick, so most pens don't. The writes-on-anything markers (like Marks-A-Lot) are good; you need a fine one, since you'll be drawing fairly small things.
The fundamental skill, on which the rest of the technique is based, is to count cards from one hand to the other. The cards are dealt with an audible snap. Each card arriving in the "to" hand lands on top of the previous cards. Between deals, each hand does a little "squaring" of the pack, to keep it from getting messy (which leads to dropping cards, losing control, etc.). Practice dealing until it is easy, smooth (except for the "snap"), and automatic.
During this, the "from" hand stays in front of your sternum, and the "to" hand swings in time with your feet (in much the way it would when you're walking normally, swinging your arms). One card is dealt to the "to" hand each time the foot on the same side as the "to" hand hits the ground. The snap of dealing is in sync with that foot hitting the ground. The whole motion should be easy, natural, smooth. Practice this until you can do it all automatically. A good benchmark is: can you do this while watching where you're going, negotiating bumps in the sidewalk, and talking?
In soft pencil (so that it can be erased), write a random word on each card, near the top (so that it can be seen over your thumb when your thumb is resting on the center of the card). Make up 20-30 cards like this. Then, do the walking (as in Step Two), saying the word on each card. The speaking of each word should begin as that card is snapped (and the foot hits), so that while the word is being spoken, you are already looking at the next card. Once you are comfortable doing this, expand the word to two, and then to a phrase. Eventually, there should be enough on each card that you have just enough time to speak it before you're ready to begin the next.
Erase the words from the cards and replace them with rhythms, written in pen. The notes and rests should be written at the top of each card (so that there are four possible positions on the card that can be used). Here's what it looks like:
Your first set should have at least one of each of the following combinations:
Do what you did in Step Three, singing "DAH" for the notes on the cards. The singing should last the full value of the note, so that the only articulation between, say, the last quarter note on one card and the half note on the next card is the "D-". As before, each card corresponds to one cycle of footsteps; the start of each beat corresponds with a footstep. For rests, don't make any sound (other than the sound of breathing in). When you finish, shuffle the cards and start again.
If you have trouble with Step Four, there are some techniques you can use to solve them. These techniques can be used for rhythms of any complexity. a) If a particular card gives you trouble, walk without dealing the cards, just looking at the problem card, singing its rhythm over and over. Once that's comfortable hold up the problem card and another, and alternate between the two. b) Make up several copies of the problem card, and several copies of another card that is easier for you; shuffle just these two sets of cards together, and use them as in Step Four.
Whenever your set of cards gets too easy, it's time to add new ones. There are two possible ways of picking rhythms. One is to just invent rhythms from scratch (for example: figure out every rhythm that's possible using notes that are one eighth-note long or longer). The other is to take rhythms from pieces of music you're working on. Hint: don't forget to include ties.
Ties can also take place between cards. This is indicated by putting a tie on the last note of a card. (You can't tie from a rest.) If the next card starts with a note, then it's tied to the previous one. If the next card starts with a rest, then you ignore the tie.
The final step is to add pitches to the rhythms you're performing. To start, alternate between two pitches, singing one pitch for each note. Rests do not affect the sequence of pitches. Once you become comfortable with the two-note alternation, add more notes. For example:
Scale fragments up&down: CDEDCDEDCDEDC... CDEFGFEDCDEFGFEDC... Double-note alternation: CEECCEECCEECCEE... Scale-related patterns: CDEDEFEFGFGAGAB... CDEFGCDEFGADEFGABE...Your imagination is the only limit!