Differences Between Papers and Textbooks
Reading journal & conference papers is MUCH different from reading a textbook... because papers are written much differently than are textbooks (and written for much different reasons and for much different audiences). While textbooks are written for students (readers who are likely seeing the ideas for the first time) to provide an easily understood description, papers are written for researchers (people who have seen and worked on these ideas for some time) to document the author's new contribution to the body of technical knowledge. Thus, a lot of the supporting background is left out of the papers... because it is assumed that the other researchers know it. Another thing that often gets left out of papers is the details of how you get from one result to another... because it is assumed that the other researchers can figure it out.
Differences Between Journal and Conference Papers
There are two main differences here:
Journal papers are longer expositions than conference papers and can therefore afford to provide more detail
Journal papers are generally better written because they go through a stronger peer-review & revision process than do conference papers and because they are often written as the culmination of a project (in contrast to conference papers which often are reporting on "work-in-progress") and therefore the ideas presented are often more completely worked out
That stronger review & revision process also tends to make the results in journal papers more "trustworthy" than the results in conference papers. I'm not saying you shouldn't believe what is in a conference paper... but you should keep in mind that it may not have been subjected to quite as thorough peer-review as a journal paper.
Two Types of Journal Papers
There are also two main types of journal papers:
These are the more common type and they are presenting some new research results that are a novel contribution to the field
Tutorial or Review Papers
These are written to provide researchers who are new to a field a comprehensive review of the field. Although they are often called "Tutorials" they are still less "tutorial" than textbooks. Hoever, some do go into the details in some depth - but some don't explain the details but rather try to link main approaches without going into the details of any of the methods.
Clearly the former is most useful to the new researcher since they give a fair amount of detailed coverage. But... both types usually provide an extensive list of references, which is an invaluable roadmap to the literature for that field!
Pitfalls to Avoid
There are two main pitfalls to avoid:
Ever-Expanding Pyramid: You start to read the paper and you are no farther into it than the first paragraph and suddenly the author says something like "... the method we propose has none of the bad characteristics that limit the applicability of the method developed by I. M. A. Goodread " and you immediately think "Gee, I don't know a thing about that method let alone what its limitations are... I better read that before I go on." So you get that paper and you get into the first paragraph of that paper and find a reference to another paper... and so on. Given that each paper has a dozen or so references, pretty soon the task of reading the original paper has expanded into reading dozens and dozens of previous papers and you never get back to that original paper.
Gotta Know Every Detail: You are reading along in the paper and you hit one of two situations: (i) there is a step in the mathematical development that you can't seem to understand how they go from one result to the next, (ii) the author uses one of those ubiquitous phrases like "... it is easily seen that ..." but to you it is NOT AT ALL easily seen, or (iii) the author uses the other favorite phrase "... as shown in  ..." and then you are back to the pyramid problem. In all of these cases there is a feeling that you can't go on reading until these details are fully understood.
How to Avoid the Pitfalls
The thing that you have to realize is that you CAN read and understand some of the paper without chasing every reference and without working out every detail. Here is how (it relies on the fact that papers are meant to be read using a "multi-pass algorithm"):
The first time you read the paper: give it a quick, high-level read (don't go to any of the references and don't worry about how the math details follow). What you are shooting for here is a basic understanding of the RESULTS & CONCLUSIONS of the paper. You don't particularly care who else did what nor how the math was used to get there. For example, in a paper on a new method for emitter location you might only want to get things like "what is the signal model used," "what is the accuracy that is claimed," "what kind of processing is needed," "what statistical estimation method was used (e.g., least-squares or maximum likelihood)", "what are the main conclusions"
The second time you read the paper: After the first read you should be able to determine if the content of the paper is worth working to understand more fully. The second time through you are going to want to pay more attention to the mathematical development, but still avoid worrying about the details that aren't immediately obvious. Remember... what you should be getting out of the math is what the results say about the problem at hand - how you go from step-to-step is much less important at this point. Worrying about the "how you got there" rather than the "what it tells you" is sort of like going to see the movie Jurassic Park and spending the whole time wondering about how they made those fake dinosaurs do all that stuff BUT missing the whole plot of the movie (well... in my analogy I AM assuming that there is a plot to Jurassic Park!). When you come out of the movie your friends are discussing the plot and you don't have a clue about that but you can sure talk about how they made the dinosaurs move! So when you see a line that says "... then by using (11) in (9) we see that..." you can just sit back and trust that the author (and the peer-reviewers) got it right and just ponder about what the RESULT MEANS! (Of course, it is likely that later you'll want/need to get down to the details... but avoid it at first)
Now, if at this point there is a need to dig farther into the paper, THEN you can go chase the references and sit down and scratch your head over the fine points of the development
Main Things to Observe
The main things from a paper that you want to be etched in your head when you are done reading it are:
What signal model is used?
What assumptions were made about the signal?
What conditions must be met in order for the method and/or analysis to hold?
What fundamental methods are being used (e.g., DFT, ACF, PSD, PDF, Bayesian, etc., etc. etc.)
What ramifications do the results have on the problem?