There are different methods depending on the the type of telescope. For prime focus use (where you're effectively using the telescope like a big telephoto lens), you need to get the camera sensor positioned at the focal plane of the scope. With telescopes with a 2" focuser, this can be done with a 2" nosepiece (like the barrel of an eyepiece). There are two options here - you can either get a 2" to T thread nosepiece, and a T-Ring for your camera brand, or you can get a 1 piece nosepiece designed for your camera brand. The latter can allow a slightly larger diameter hole than the T ring standard, which can reduce vignetting (especially with full frame cameras).
It's likely that the university should already have the required adapters and reducer/flatteners, so check with them. You may only need to get a Nikon T ring, if they don't have them.
Some (refractor or reflector) 1.25" focusers include a T thread as standard - you may be able to unscrew the end of the eyepiece holder to reveal a T thread that yoy can attach the T ring to directly.
However, If you're talking university scopes, it's likely that they'll be SCTs. In this case, they're usually fairly slow (typically f10) and you may want to use a reducer/flattener to reduce exposure time and increase field of view, as well as producing a flat field (many telescope designs actually have a curved focal plane). In this case, getting the correct spacing between the reducer/flattener and the sensor is critical to get good results, so there's usually a standard adapter tube (with an SCT thread at one end and a T thread at the other) which is designed to give the correct spacing. One end screws to the back of the SCT (or to the reducer/flattener, which then screws to the back of the SCT) and the T ring and camera attaches to the other end.
(Spacing is also likely to be critical if the scopes are advanced SCT designs with corrective optics already built in).
It's likely that the university should already have the appropriate adapters and reducer/flatteners - check with them to find out. You may only need to get a suitable T ring for your camera.
If the scope is on an alt-az mount, field rotation will limit you to around a 30 second or so max exposure (it varies depending on latitude and where you're pointing - although an alt-az mount can track fine for visual use, the field of view gradually rotates as you track an object across the sky, and this will cause trailing as the image appears to rotate around the center).
If the scope is on an equatorial mount (or the alt-az mount is running in equatorial mode on a wedge) field rotation isn't an issue - but you may need an autoguiding setup for long exposures to correct for drift.
[Meade also had - and may still have - a derotation system that compensated for field rotation in alt-az mode. If that's the case where you are, you'd need to check with someone that knows a bit more about it].
If you want to take photos with exposures over 30sec - which is usually the limit for camera exposure settings - then look at one of the cheap intervalometers on ebay. They run around $15 or so, and allow you to do multiple long exposures using the "B" exposure setting in manual mode. Just make sure you get the correct one for your camera model. Functionality is usually identical to the official Nikon model, and appearance is usually the same other than branding (Having had both the official and 3rd party versions for my D300, I suspect Nikon probably OEMed theirs from the same supplier - but the eBay version was a fraction of the cost).
Alternatively, if you're going to be using a laptop, you may want to look at "Backyard Nikon", a shareware control program for astrophotography. You may need some additional hardware to allow longer exposure control; not sure.
In any case, you probably want to look at the freeware "Deep sky stacker" or "Deep sky stacker live" programs - they let you "stack" multiple exposures of the same target to reduce noise and bring out more detail (since the noise is random, but the image isn't, combining multiple exposures (often tens or hundreds) can dramatically reduce noise and give a much smoother final result.
You will probably want to turn in camera long exposure noise reduction off and shoot some dark frames instead - LENR basically takes a second exposure with the shutter closed, and then subtracts it from the main exposure to reduce "fixed" noise. By taking your own dark frames (with the lens and viewfinder covered - doesn't have to be on the scope, just at the same temperature), deep sky stacker can do the subtraction instead, you can get a better result (averaging several together) without taking as much time (you don't end up doubling the exposure time for every shot).