Hypomating is a wonderful feature available to everyone! You can select your own stallions/mares from a dropdown list or type in the ID # of any stallion or mare you do not own.
If you have a hard time visualizing the possible results from a breeding, you will probably benefit from using hypomating frequently. This can tell you the possible genetic outcomes in your foal. It's not always exact, but offers you a visual estimate of what the foal may be. If it says you have a 75% chance of Xx (where X/x can represent any gene) a 25% chance of xx, don't just assume that 75% chance guarantees the Xx. It is just a chance, and chances don't always come out the way they have the highest probability to.
The hypomate will only work if you have at least genetic ratings purchased. If you have ratings, you will not see the exact percentage breakdowns, as listed above, but will see a side-by-side comparison of your mare's genes to the stallion you have selected. While this doesn't tell you anything more than you can see on their pages, it is sometimes helpful to see the genes next to each other rather than on two individual pages.
Genes must also be public in order to be seen on the hypomate. This includes your own horses, since the hypomate pulls from publicly available information.
If you have the Advanced Hypomate skill, you will also see a section that tells you information about the stallion and mare's foal history. This counts the number of Genetic Merit foals they have produced and the percentage of colts that have been gelded. While those can both be helpful, the most important thing to look at here is the Average Foal Potential (AFP).
AFP is the average maximum potential of all non-gelding and non-steeplechase offspring. A stallion must have a least 5 eligible foals before he will show an AFP. The offspring do not actually need to be maxed yet! If a stallion has 5+ foals in his first crop, this will be visible as soon as they're all born. The higher the number here, the better. It is generally accepted that a stallion needs to have an average of at least 30 to be considered stud quality. However, the best studs (those with Silver and Gold SIP potential) will have an average of 35, 40, or even higher. The higher a stallion's average is, the more likely you are to get a stakes-quality foal.
The Improvement Over Dam (IOD) section is a relationship between the AFP and the average potential of the mares he has been bred to. For example, if a stallion has an AFP of 40 and a 5 Improvement Over Dam, he has produced (roughly) 40 potential foals out of 35 potential mares. A higher number here is usually better, but low numbers can be misleading. A stallion who is bred to mostly lower potential mares will almost always have a higher IOD. A stallion who is bred to mostly mares of 50+ potential will have a relatively low (or negative) IOD simply because there isn't much room for improvement. IOD should rarely be considered on it's own, but instead alongside AFP. A stallion who has a 32 AFP and 20 IOD is a much stronger prospect than a stallion who has a 40 AFP and 1 IOD. The first stallion here has clearly produced stakes-caliber foals out of mares who are at the lower end of allowance. The second stallion, though he is throwing stakes-caliber foals, is likely benefitting simply from breeding to higher quality mares.