The analysis of astronomical data is commonly referred to as "data reduction". Data is analyzed (or "reduced") using software on a desktop computer. The most commonly used software package for optical and infrared data is the Image Reduction and Analysis Facility (IRAF). Learning the basics of IRAF is important if you expect to work with optical or infrared data. The IRAF homepage provides a tutorial, and many others are available on the web. IRAF can be downloaded and installed for free. Another commonly used set of software is IDL, for which a license must be purchased (usually a department-wide license is available).
During day-to-day research, you will frequently need to manipulate data from text files and perform various mathematical tasks. Learning some kind of programming or scripting language is necessary to do this. For computationally intensive tasks, fortran or C are options, but otherwise I use perl whenever possible, which is much more user friendly and versatile. Like Unix and IRAF, perl (or some equivalent scripting language) is very important to learn.
If you are responsible for installing the software on your computer, then this task is much easier with Fink.
Detailed advice specific to an astronomer using a Mac is available here.
Here is a list of the primary professional astronomy journals. ApJ is the most prestigious of these journals and its articles generally have the highest quality and impact. A scientist from any country can publish an article in any of these journals, but the papers in a journal tend to be authored predominantly by scientists from the country in which the journal resides, such as the US for ApJ and AJ, UK for MNRAS, and Europe for A&A.
Using the NASA Astrophysics Data System (ADS), you can search the astronomical literature for articles according to various criteria, including author name, title, subject, year, and refereed/non-refereed. For instance, if you want to see a list of the papers written by an astronmer, enter "Smith, J." in the author field. When the list of papers appears, you can then download the papers. For newer articles, your computer will need a license for the journal in question, which is usually available transparently if using a computer at an astronomy department. Older papers usually don't require a license and are free.
Finally, an important resource for publications is the archive of astronomy preprints, known as astro-ph. The time between when a paper is accepted for publication by a journal and when it appears in a printed issue of the journal is usually several months. To more quickly communicate their results to other scientists, most astronomers post a copy of their paper on astro-ph as soon as it is accepted for publication by the journal. (Some astronomers post the submitted versions of their papers before they have been accepted for publication, but I don't recommend this.) A new list of posted papers appears at astro-ph every weekday morning. It's good to develop a habit of checking astro-ph on a regular basis to keep up to date on the most recent work in your field.
NED is similar to Simbad, except specialized for extragalactic sources.
The Digitized Sky Survey (DSS) contains electronic scans of photographic plates of the entire sky that were taken decades ago. The image quality isn't good by the standards of modern telescopes, but it does cover the whole sky and is often useful for planning observations (e.g., making finding charts) and for the measuring proper motions or variability relative to newer images.
The Sloan Digitized Sky Survey (SDSS) is an optical imaging survey of 1/4 of the sky (modern version of DSS).
In 2010, the Wide-field Infrared Survey Explorer (WISE) obtained images of the entire sky at four mid-infrared bands (3.4, 4.6, 12, 22 um).
The Deep Near Infrared Survey of the Southern Sky (DENIS). Similar to 2MASS, except in the I, J, and H bands instead of J, H, and K and only for the southern hemisphere.
Most space observatories (Hubble, Spitzer, and Chandra) and newer and larger ground-based observatories (ESO/VLT, others) that are supported by public funding maintain archives of their data, or have plans to do so. The scientist for whom the data were obtained usually has a proprietary period of 1-2 years; after that, anyone can download and use the data.
The Infrared Science Archive (IRSA) provides an interface for accessing archives for many infrared and submillimeter missions, such as IRAS, ISO, 2MASS, SWAS, SDSS, MSX, and Spitzer.
The AAS hosts 2 conferences each year, which are usually the largest astronomy meetings in the country. A comprehensive list of all meetings in astronomy that are planned in the next few years is found here. It's good to check this once in a while to see if there are meetings planned for the next year that you would like to attend.
Mauna Kea on the big island of Hawaii hosts the greatest collection of telescopes in the world. The atmosphere above Mauna Kea typically is very stable and allows for sharp images, or excellent "seeing". Water in the atmosphere absorbs light at many wavelength ranges of the electromagnetic spectrum (e.g., mid-IR, or 10um), normally preventing observations of stars at those wavelengths. However, those observations are often possible from Mauna Kea because the atmosphere above it is very dry and thus suffers from less water absorption. These telescopes are operated by various consortia of governments and institutions. As part of the agreement with the state of Hawaii for allowing construction of these telescopes, the University of Hawaii is given a share of the time on all of them. Chile has a similar arrangement for all telescopes built within its borders.
3.0m NASA Infrared Telescope Facility (IRTF) is available for use by any professional astronomer. Half of the time is allotted for solar system research and the other half for the rest of astronomy. This telescope has a wonderful near-IR spectrometer (0.8-5um) called SpeX and offers remote observing from your home institution.
3.6m Canada-France-Hawaii Telescope (CFHT)
3.8m United Kingdom Infrared Telescope (UKIRT)
8m Gemini North (National Optical Astronomy Observatory (NOAO), United Kingdom, Canada, Chile, Australia, Argentina, Brazil, University of Hawaii) Most of its observations are performed by observatory staff (queue observing) rather than the astronomers themselves (classical observing).
8.2m Subaru Telescope (Japan)
2x10m Keck Observatory (Caltech, the University of California, NASA)
15m James Clerk Maxwell Telescope (JCMT) (UK, Canada, and Netherlands)
8x6m Submillimeter Array (SMA) (Smithsonian Astrophysical Observatory and Taiwan)
Major observatories are located on several mountains in Chile.
4m Blanco Telescope was one of the premiere telescopes in the world at one time but now is somewhat old with image quality that is lower than newer, state-of-the-art telescopes.
4.1m SOAR Telescope (on nearby Cerro Pachon) (NOAO, Brazil, the University of North Carolina, Michigan State University) SOAR was recently constructed and offers excellent image quality.
several smaller telescopes run by SMARTS consortium
8m Gemini South is on Cerro Pachon next to SOAR.
Las Campanas Observatory (LCO) is operated by the Observatories of the Carnegie Institution of Washington (OCIW). Because the altitude of Las Campanas is not particularly high, the site isn't as good as Hawaii or Paranal for mid-IR observations.
2x6.5m Magellan Telescopes (Carnegie, Harvard, Michigan Arizona, MIT) No ground-based telescope outside of Antarctica has better seeing than Magellan.
2.5m DuPont Telescope
1m Swope Telescope
3.5m New Technology Telescope (NTT)
several smaller telescopes
3.5m Wisconsin-Indiana-Yale-NOAO Telescope (WIYN)
2.3m Bok Telescope (University of Arizona).
several other 1-2m telescopes
6.5m MMT (SAO and Arizona)
1-2m telescopes, an optical/IR interferometer, and gamma ray telescope
other smaller telescopes
other smaller telescopes
Texas and New Mexico
2.7m Harlan Smith Telescope
other 1-2m telescopes
2.5m Sloan Digital Sky Survey Telescope
other smaller telescopes
3.9 m Anglo-Australian Telescope (AAT)
1.2 UK Schmidt
4.2m William Herschel (UK, Netherlands, Spain)
2.5m Isaac Newton (UK, Netherlands, Spain)
1.2, 2.2, 3.5m Calar Alto Observatory (MPIA, Spain)