Mini-carnations? Depends on if it is a florist carnation, or a border carnation. They are very different. Both have limited bloomtime. Both need much deadheading to extent bloomtime. The florist carnation is not hardy.The border is. There is also a carnation called a pink. It is used more as an annual then perennial, because it is not reliable. Sometimes it comes back, sometimes not. I would enjoy your mini-carnation while it is in bloom, then set it aside when it is not. Water and care for it. Give it plenty of light. It will probably bloom a second time in the fall, or next spring. They are that unpredictable.
I think that by Mini Carnations, you mean Dianthus, also known as "Pinks". They are great plants for beginners. They are easy to care for, and have great flowers for containers. Get the best potting soil you can buy. Mix in some time release fertilizer and moisture retaining granuals. Some potting soils already have these added, so try to find that when you buy you soil. You will water less, the plant will stress less in-between watering and you will never have to fertilize again. When you water, thoroughly soak the soil. Don’t get water on the plant. Then let the soil dry before you water again.
Don’t over water them. Dianthus need sun to flower well.I have mine on the East side of my house, so they are shaded from the hot afternoon sun. I have had them there for four years. Unfortunately, Dianthus don’t like humid conditions. So in the South, they are concidered annuals. They will not come back a second year.
One place that has fresh flowers and really cheap is Costco. If you have one around your area check them out. Another idea is to use flowers such as mini carnations instead of small rose buds in corsages. They are a lot less expensive. Alstroemeria is also inexpensive as are mums. And mums come in a variety of shapes. They also last along time.
You can find these type of flowers in bouquets sold at grocery stores. One grocery in the Chicago area that has a lot of loose flowers is Jewel. Check out your local grocers to see what they have. If you have hard water invest in a water filter and make sure you use flower food that is usually with the bunches. Mix exactly as the package says!
If you want to start from seed gently press the seed into a pot of good potting soil that is damp not soggy. Put the pot inside a plastic baggie and keep under a 40 watt shop light and germination will occur in about 2 weeks. When the seedlings have their 2nd set of leaves, you can gently prick the seedlings out and plant them in separate pots. You can plant them outdoors after all danger of frost is over. Make sure you place the seedlings in a place out doors, still in their separate pots, safe from direct sunlight and extremes in wind, temperatures and rain for 10 days.
This prepares the seedlings for being planted out directly in the sunlight. They will then need partial shade to full sunlight and watered at least once a week. Apply a general 10-10-10 fertilizer every 10-14 days. Pinch off spent flowers to encourage more blooms.