[Edit: This was migrated from programmers.stackexchange.com so this answer assumes the candidate is a software developer. However, many of the concepts are generic.]
Interviews with HR or screening firms are looking to:
- Verify your experience. Have you used language X or library Y? If so, for how long? What kinds of projects have you done?
- Determine what are you looking for. For example, do you want to learn something new or build on what you are doing? Do you want to move to a team lead role?
- Determine whether you can communicate. Can you explain what you were doing and where you want to be? If the (spoken) language is not your native language, are you proficient enough to operate in a company speaking that language?
As you say, the aim is to determine a fit. The interviewer is rarely technical and is usually looking to check boxes only. Some advice:
- Answer questions succinctly then ask if they want more information.
- Have answers to questions like "Tell me about yourself" and "Where do you want to be in five years' time?" worked out beforehand.
- Know your recent achievements, including those outside work whether they be technical (e.g. a blog or open source work) or otherwise (e.g. coming second in the work soccer tournament).
- If you are excited or passionate about what you do, make sure you convey that. It may sound silly, but smile as you talk on the phone. It will make a difference.
- If you know who will be interviewing you beforehand, do an Internet search and see if you can find more about them. LinkedIn is great for this, too.
The interview will usually be short - fifteen minutes or perhaps half an hour. As you are wrapping up and straight afterwards:
- Ask what the next step is. Will they contact you? If so, who, by what means (e.g. E-mail, phone) and when.
- If you do not know them already, get the interviewers' names. It is a personal touch and will help with the follow up.
- Take notes about anything unusual or notable afterwards, such as "Have you used obscure framework X?" and do some follow up research if you are interested in continuing.
You say the interview is with a psycologist. From my experience, psycometric testing is usually expensive so they will usually screen you first but, if it is a psycologist, the questions may be even more unusual. Do not get nervous about these kind of tests or questions - you have spent your whole life practicing to be you. The best preparation is a good night's sleep beforehand.
As for asking about the company, either they will tell you or they will not. If they will tell you, ask:
- The company's name
- (if you are unfamiliar with it) it's industry and main customers.
- Which part of the company would you work for.
- The role (such as developer, pre-sales, consulting, etc). If you are unsure, ask for a work breakdown, e.g. 75% developing, 20% training others, 5% admin.
- Who the role reports to (e.g. team leader, remote or local, team size and composition).
Have the interview even if you are happy in your current job. It gives you vital interview experience, exposes you to others and (might) get you an even better job. As long as you are honest and open with them, politely refusing an offer if it is not what you want is not a negative.