What is a person with these placements like? Sun: Aries Moon: Capricorn Venus: Aries Ascendant: cancer?

Your rising sign is Cancer which is ruled by the Moon and yours is in Capricorn, an earth sign so you're likely to react to people in a practical sort of way, or in ways that could lead to concrete gains to be had for you. Your Moon could be in your 6th or 7th house so which ever house it's in is where what you experience here directly influences the way you grow and mature as a person in your life. If your Moon is in your 7th house that shows that partnerships and meeting people in any one to one situation will direct the way you mature; if it's in the 6th house, that's the house of health and daily routines so this is where you learn so much about yourself and in fact it's likely to be your daily routine that gives you some sort of feeling of safety and security. Similarly if it's in your 7th House, the Moon there shows you probably get some sense of security from being with your partner.
Your Sun in Aries is 3 signs away from Capricorn, where your Moon is so they may be square to each other if the degrees of the Sun in Aries and the Moon in Capricorn are within 8 degrees of each other. If they are square then your steadfast and disciplined Moon may react negatively to your Aries Sun's needs for freshness and newness in your life and especially in the area of life depicted by the house your Sun is in and the house with Leo on the cusp. The house with your Moon in will somehow be linked with the house your Sun is in and maybe one hinders the other in some way.
Similar things could apply with your Venus in Capricorn, (maybe conjunct your Moon), and your Sun in Aries. The signs your planets are in only show a very basic style the planets use and a lot depends on how the planets are aspected. Venus in Capricorn can be very loyal and faithful but also be overly so and if Venus is in your 6th house that could be about being overly orderly and disciplined in health matters, or daily routines - everything has to be neat and orderly etc. If Venus is in the 7th house, everything has to be in good taste and maybe a sense of your own beauty comes from your partner in some way, or you tend to look upon them as some sort of God or someone to be worshiped and adored. Partnerships for you are something that can make you feel complete maybe.