It is absolutely possible to avoid plagiarizing other people's work if you make sure to include in-text citations for quotes and paraphrasing and follow them up with a citation on your Works Cited (MLA) or References (APA) page.
When quoting another person (i.e. using their exact wording) make sure to put that quote in quotation marks to show where their words begin and end.
After the quotation, put a citation indicating who and where the quote is from. The citation will typically include the author's last name, the year of publication, and the page number the quote came from. This applies to both MLA and APA style
An example of a quote in APA style: "Mindfulness means understanding that all you ever really have is the present moment, and practicing a new way to inhabit and observe that moment: with a focus on allowing, accepting, and being fully aware of whatever you're experiencing" (Pittman & Karle, 2015, p. 193)
If you're not using their exact words but are putting their ideas into your own words, you still need to cite the source. This is known as paraphrasing, and it is the preferred way to use other sources as it demonstrates you understand the source you are using. A citation must be included anyway.
An example of paraphrasing the quote above in APA style: Living in the moment is the foundation of mindfulness, which means paying attehntion to what's happening around you with intention. (Pittman & Karle, 2015)
Notice the difference? The quote citation includes the page number but the paraphrase does not. Both citations require the author information and publication year.
Patchwriting is the process of mixing up another person’s words with your own, changing just a few words when the language or structure is essentially the same. Patchwriting is considered plagiarism.
For every in-text citation (immediately after a quote or paraphrase), you'll need an accompanying reference or works cited citation on a separate page. Here is how that same source would be formatted in APA style:
Pittman & Karle. (2015). Rewire Your Anxious Brain. New Harbinger Publications, Inc.
Notice that the beginning of the citation above matches the information you put in your in-text citation.