The first way of doing this is to approach your board and request a trial match to have a look at some of the local talent. There is no guarantee that the board will accept this proposal. They may be against the idea if the club is in a difficult financial position, or if they feel they would not be able to add any worthwhile players from such an event. If they do accept the idea, however, you will have the opportunity to evaluate a high number of players who are without a club, who will most certainly be interested in joining your club.
The second way of doing this is to offer a player the chance to train with your club on a trial basis. The time frame of this trial can be anything from one week to four, and you may offer the player further trial opportunities in the future. There is no limitation in this regard. This is a good opportunity to see how a trial player fits into the club. Does he have the kind of personality which fits well with the rest of the squad? Is he professional in training? Does he have the ability to be a competent signing for you? Your assistant manager and coaches can offer information on this upon request.
While you can offer any player a trial, it is worth noting that players under contract at other clubs may be denied a trial period at your club. You can't just go and take Lionel Messi on a trial from Barcelona whenever you feel like it! It is also worth noting that not all players may be happy to participate in a trial run at your club. Zlatan Ibrahimović famously turned down the opportunity to go on trial at Arsenal many years ago.
While a player is on trial at your club, it is important to keep note of his training ratings. This is a brilliant new feature this FM which allows you to see the performance level of each player in each week of training. While a player on trial may just be unfortunate in that he would be having an off-week while at your club, training levels are good indicator as to whether a player is capable of being a useful part of your club in the future, so keep note of this.