I often work with cyclists that are brand new to triathlon or time trialing and the "aero" position. With up to 60% of on the bike drag coming off the torso alone the first thing I get them to understand is the extreme disadvantage of competing on a traditional road bike. The (very expensive) bike itself usually accounts for less than 10% of the drag; it is the position that makes the difference. Installing clip on aerobars on your road bike is not a bad place to begin the acclimation process, but a road bike is not designed for this and should not be attempted to be made into a TT or tri bike.
Initiating the aero position can, unfortunately, be a painful process if not done correctly and incrementally. For starters, the heavy head, which was sitting more upright upon the shoulders (as it was made to do), is now suspended out in front which can create a lot of tension, fatigue, and soreness in the neck in shoulders. As the torso goes down, the head must come up to see the road flexing the cervical spine. The muscles of the neck, trapezius, and mid-back are now over-worked supporting and holding the head in this relatively fixed position. This is further exacerbated by the nervous muscular tension of being in a new and unfamiliar position, on a new bike, with a completely different cockpit (where are those brakes!). To find comfort and relief the cyclist often sits up which is akin to putting the brakes on. They end up spending most of their time back in an upright position on the pursuit bars, totally negating the aerodynamic advantage of they just spent a lot of money to purchased.
The TT/tri bike position is more forward in relation to the bottom bracket and this utilizes a different mix of the pedaling muscles. It requires time to get acclimated and get the legs firing properly in this new position, and power may initially drop slightly. If the athlete spent most of their time "sitting up" in the hoods, or was previously set in a more upright position on their road bike, the lower torso angle will also stretch muscle chain of the low back and hamstrings. If this muscle chain was already tight (which is often the case) in the new position, discomfort or even over use injury can occur. Saddle pressure also changes quite drastically in the new position. Instead of sitting more upright on top of the saddle, the pelvis is rotated forward onto the nose of the saddle. Weight is distributed at an angle creating different pressure points, especially in the perenium. For this reason a saddle change to one designed to accommodate a low torso angle is often applicable, or at the very least a change in saddle tilt to a lower nose. Even if you are fitted properly by a profession an acclimation period will be necessary.
When making the investment in a TT/tri bike an assumption can be made that the cyclists wants to be fitted in an "aggressive" position to go faster. The cyclist themselves may ask to be in as "fast" a position as possible not knowing the implications of this; after all they want to get their money's worth. Unfortunately this often lead to a serious case of buyer's remorse after a few rides. They may find themselves sitting up for most of their ride or even a return to their comfy by comparison road bike. There is a solution to this level of discomfort. Fitting should be a progression, never going from one extreme to another. The good thing about bikes is that they are incrementally adjustable allowing the body to stay relatively comfortable while acclimating over time.
If you are currently riding a road bike and want to progress to a TT/tri bike, I recommend starting with a set of clip-on aerobars. No, as I wrote above road bike is not designed for this. It does not allow the low (aggressive) torso angle and this should not be attempted as it makes the bike handle in an unstable "twitchy" manner. But it is valuable as a temporary and first step (not to mention inexpensive). And for triathletes that cannot afford a tri bike this may be the best place they can spend their money. Although not as low or stable as a tri bike the position is often lower than the drops and also reduces overall surface are to the air. It is important to note that the addition of aerobars will require being fitted to a more forward position and adjustment of the road bike. I like to set the athlete up in approximately the position they would ride in the drops. Now if you are not acclimated to riding most of the time in the drops this should be accomplished first. I advise being able to ride comfortably in the drops over the speed of 15mph before thinking about adding aero bars to a road bike. Why 15mph? That is approximately the speed at which aerodynamic drag is mitigated and it makes more sense to sit up; which is why cyclists do not ascend in the drops at low speeds.
Begin by spending as little as 5 minutes at a time in the aero position and gradually increase from there. You may start with 5 minutes aero and 5 minutes sitting up. Go to a parking lot and get acclimated to the handling characteristics of being in the aero position and practice getting to your brakes quickly. Triathletes are often incensed by the "no aerobar" rule of many group rides; especially if they have just one bike. But this rule is a very valid safety precaution in that you cannot get to your brakes quickly enough when riding in close proximity to other riders. Once you can ride the duration of your ride over 15mph in the aerobars you can think about moving lower. It is important to note here that properly setting up the time trialist or triathlete is a very tricky thing to do; and it requires a trained and experience fitter. For instance simply lowering the aerobars by removing spacers will close up the hip angle essentially putting the knees into the torso and creating a very uncomfortable position. When adjusting one parameter, such as bar height, all three must follow. In other words in or order to go lower you must also bring the seat and cockpit forward as well as raise the seat slightly.
Clip-on aerobars are a relatively inexpensive way to get adjusted to the position and a good first step, but if you want to fully optimize your position a TT/tri bike is required. Not only does it allow for a lower and more aerodynamic position the bike is designed to be stable in this position.
When you are ready to put down the credit card on a more aerodynamic bike, let the sales person know you are new to the aero position. This should tip them to put you in a less aggressive position, or one slightly lower than your present position. This means the aerobar pads will be almost level or just below the saddle. It should feel somewhat strange, but not horribly uncomfortable. Realize that this position is a good starting point but you will want to get more aggressive as your body dictates. Simply put, most of your wind resistance comes from the torso and, by lowering the torso position, you will increase speed. I like to take several progressions from this starting point for a newbie. An initial fit with several shorter follow-ups can greatly increase aerodynamic efficiency without sacrificing comfort and power to a large degree. Some comfort adjustments such as saddle tilt can be done by the athlete themselves, but I carefully mark all positions on the bike with tape or a paint marker. This also comes in handy when the athlete has to ship their bike across the country for a race, and can reference where the components were prior to be disassembled..
Your fit should also be predicated on your racing. A triathlete racing mainly sprints or Olympic distance events may be able to tolerate a more aggressive position for the shorter bike split. An Ironman athlete simply must be in a more comfortable position. I may even have two positions marked for an athlete who races both these event types; one for speed and the other for comfort. Pad width, position of the forearm pad, and saddle tilt may need to be adjusted for comfort over aerodynamics and leverage.
Spend time stretching, strengthening, and rolling the lower back and hamstrings. These muscles often become tight in multi-sport athletes creating further difficulty in positioning as well as affecting their run off the bike. Strengthen the muscles of the upper back. Remember that your position and comfort trumps just about anything else. I have had numerous athletes come through our door on 10k+ TT/tri bikes that would be better served on road bikes. If you suffer from a condition such as degenerative disk, nerve impingement, stenosis, or bone spurs note that the lower position generally makes these worse and an more aero bike may not be a good purchase.