Nearly everything in astronomy ultimately comes down to observations. You, yourself, have the capability of proposing, making, and analyzing observations even if you've never done it before!

First things to consider:

1. What do I want to observe? Note that many of the things you might want to observe may not be practical to observe. Bright objects are easier to observe than faint objects. High surface-brightness objects are easier to observe than low surface-brightness objects. Imaging is easier than spectroscopy. This doesn't mean that the observing projects themselves will be easier if you choose bright, high surface-brightness images, but you will have more options to be able to go after "easier" targets than harder targets since you can use bright time (when the moon is out) and smaller telescopes that are under-subscribed.

2. When are my objects visible? In many cases, if you have a choice of objects you will just choose the subsample of objects which are up whenever you get time. In some cases, you may be interested in a very particular object. Do NOT propose to observe for an object when it is down. This seems simple, but there are anecdotes of people trying to observe the Magellanic Clouds from Arizona. It's physically impossible to observe objects that are farther north than -90+latitude in the Northern Hemisphere objects and farther south than 90-latitude in the Southern Hemisphere. Also, know the RA of the Sun. It's, by definition, 0 at the Spring Equinox and advances two hours each month throughout the year. An object that is at the RA at midnight can, theoretically, be viewed all night long (at least in the summer -- not so much in high latitude winters where nights can be longer than 12 hours!)

3. Where is the moon in relation to your object? If you're doing bright-time observations this is an extremely important consideration. You can tell quickly by using something like JSKyCalc

4. What instruments are available and what are their strengths and weaknesses? Your first time observing, this can't be as much of a consideration, but eventually you'll get a feel for the quirks associated with different instruments. If you're doing time series, you'll want fast read-out CCDs. If you're doing wide field observations, you do not want to use a small-format CCD, etc.

5. What filters/wavelength ranges do I need? Check to make sure you instrument is sensitive to these. Sometimes, you may have to pack your own filters if the observatory doesn't have exactly what you're looking for.

6. What if it's cloudy, the seeing is poor, or I don't have objects to observe all night long? It's a good idea when making your observing program to account for all these things. If your project is dependent on sub-arcsecond seeing, it's best to have a back-up program in case the conditions are poor. Likewise, there are some projects (like differential photometry) where intermittent cloudiness isn't as big of a deal as for other projects (such as flux-calibrated spectra or absolute photometry). If what you want to observe doesn't rise until halfway through the night, try to come up with some earlier targets yourself or ask some of the veteran observers if there are objects they'd like to get data on. Almost every observer in the department has a bucket list waiting for such scenarios and some (namely Joe Patterson) have observing programs which can be done in very poor conditions.