Many blogs have very specific guidelines for choosing a journal for publication, often with heavy emphasis on impact factors, journal indexes, and the author guidelines provided on each journal's website. My advice is less complicated, and assumes that you are a good researcher who reads widely in your field of study. Some researchers start the process of selecting a target journal early in a research project; this can help focus your project, and influence the data you collect and the subsequent analysis. Other researchers choose a target journal later in the process, especially if their results are unexpected.
Step 1: Compile a list of relevant research articles, and the journals that published them
All researchers should have a semi-organized collection of papers that are relevant to each of their research projects. Search through this collection to find the papers that are most similar to what you hope to publish. Most journals are very interested in publishing papers that expand upon work that they previously published. For example, your work may provide updated treatment guidelines for a medical condition that is often covered by Journal A; your work may provide additional information about a biochemical pathway that is frequently discussed in Journal B; or your work may use a technique that was first described in Journal C.
As you compile a list of similar articles and associated journals, also consider the papers that are referenced within these articles, and papers that have cited these articles. Two great resources for finding related papers are Connected Papers and Microsoft Academic Search. Carefully review these similar articles—noting their date of publication—and consider whether your work would be of comparable quality and importance at the time of publication. This will help you rule out journals that are unrealistic or a poor fit, and rank the others as "optimistic", a "good fit", or "less competitive". Never submit to a journal that you do not respect.
Step 2: Decide on your priorities
Some researchers will prioritize getting published in a high-profile journal. This might involve a lengthy review process, making significant revisions, and (perhaps) still being rejected. Other researchers need or want to have a paper published quickly, which might involve submitting to a reputable but less competitive journal. This might still involve a prolonged review process, significant revisions, and (perhaps) still being rejected. In some fields, the rise of increasingly prestigious open access journals that prioritize rapid publication may provide the best of both worlds.
In any event, you should clearly map out what you want and need to move forward in your career, and when specific events need to happen. Do you want or need to publish before defending your thesis? Before entering the job market? Before applying for research funding? Before applying for tenure or promotion? Realistically, when do you need your paper to be published? Would "accepted for publication" or "in press" be sufficient?
Then you need to consider the kind of journal that is required for your desired outcome. Will the people making decisions about your career be satisfied with any reputable peer-reviewed journal? Or will publication in a "top tier" journal be required? One metric that reflects a journal's prestige is its "impact factor", which is the average number of times an article published in that journal (within the previous two years) is cited per year. Impact factors are available through SCImago Journal & Country Rank or through a simple Google search like "impact factor endocrinology journals". A higher impact factor indicates more citations and more prestige.
Consider whether you have the time and desire to aim for a more prestigious journal, and if rejected, then submit to another journal. Alternatively, you may prefer to start with a reputable journal that offers a better chance of acceptance, and potentially have more time to spend on other research activities. Based on your priorities, you can further narrow your list and rank the possible choices.
Step 3: Learn more about the journals you are considering
Go to each journal's website and look for links like "Journal info", "Aims and scope", "About us", and "For authors". Read carefully—starting with general topics like "Journal info" and "Aims and scope"—and consider whether your research project is a good fit. High-profile journals often emphasize novel or immensely thorough studies, while other respected journals focus on well-conducted research within a certain field of study. You can only submit to one journal at a time, so do not waste time submitting to a journal that does not cover the type of work that you do.
As you read through each journal's website, look for information about how long it takes to receive a decision about a submitted manuscript. Some journals will highlight that they aim for "rapid review and publication." This is especially true of open access journals and the traditional journals that compete with them. Open access journals will publish an article online within a few weeks of acceptance (once the paper has been edited and formatted for the journal), since they do not need to wait to bundle multiple articles into an issue. Some traditional journals now also publish articles online before a new issue is released.
Open access journals also tend to be transparent about the time it takes to go through the publication process. PLOS One reports a median Time to First Editorial Decision (Rejection or Peer Review) of about 13 days, Time to First Decision of ~45 days, Time to Final Decision (Rejection or Acceptance) of ~90 days, Time to Acceptance of ~150 days, and Time to Publication of ~170 days. These are median numbers, so individual results will vary.
Let's consider a traditional journal for comparison. The Journal of Ornithology reports 60 days from Submission to First Decision (compared to ~45 for PLOS One), and 178 days from Submission to Acceptance (compared to 150 days for PLOS One). The Journal of Ornithology publishes 4 issues a year, and publishes articles online before a new issue is released. For journals that do not publish online before a new issue is released, a paper accepted for publication is often not included in the next issue. This can easily add several months to the time required for a paper to be published, indexed, and searchable online.
As you consider each journal on your list, think about your career goals and when you need your paper to be published. Balance the chance of your paper being accepted for publication by a journal with a certain impact factor, with the time you might lose if the paper is rejected.
Step 4: Consider the details for submission and publication
Publishing in a reputable open access journal can be very appealing because accepted papers are published online very quickly, and are freely available to anyone with internet access. However, since open access journals don't charge subscription fees, they typically charge authors for publication. The current publication fee for an article in PLOS ONE is $1695 USD. The Journal of Ornithology was founded as a traditional journal in 1853, but now considers itself a "hybrid journal"; authors can choose to pay a publication fee (currently $3260 USD) to make an article open access. Even without the open access option, traditional journals may require authors to pay a fee per page (perhaps US $100-$250) and/or a fee per color page (perhaps US $150-$1000) to offset the cost of printing physical copies.
These costs may influence your decision to submit your research for publication in one journal over another, but be sure to consider all of your options. As open access publishing becomes more common, institutions and grant agencies are providing funds specifically for open access publication fees. Some open access journals and traditional journals have funds available to help cover publication costs for researchers from developing countries, or researchers with no alternative funding sources. The most prestigious journals are most likely to have funds available to help authors with publication costs, so don't let these costs deter you from submitting your work to a journal that is otherwise a good fit. However, you should be prepared to provide the necessary paperwork upon submitting your article for publication.
If you are considering a premier journal (e.g. "Cell), you should also consider the more specialized journals produced by the same publishing house (e.g. "Cell Metabolism") that may be appropriate for your work. If the premier journal determines that your work is of high quality, but insufficiently novel, you may be able to transfer your article to the more specialized journal for consideration. This can reduce the risk of submitting to a high impact journal, since the more specialized journal will often save time by using the remarks submitted by the initial reviewers.
You should also consider the information provided for authors about manuscript format, length, figures, tables, etc, and evaluate whether these guidelines will allow you to present your work effectively. Finally, if you have any important questions that are not answered by the journal website, you should contact one of the journal editors. Editors will hold your work to high standards, but they generally wish you well.