There are two basic types of usages costs associated with BigQuery: query costs and storage costs.
The main costs associated with using BigQuery are the query costs. In BigQuery, queries are billed according to how much data is scanned during the course of the query, and the rate is $5 per TB, although the first 1 TB is free each month. Queries can be more expensive as they become more computationally intensive.
While most of the cost is suprisingly low, it is always important to think carefully about your queries and to make them as efficient as possible. For example, if you want to derive summary information about all ~20,000 genes, you could do that with a single query that might cost a few pennies, or you might write a less-clever query that returns information only about a single gene and then programmatically loop over all genes, running that single-gene query 20,000 times. Your overall query costs using this less-clever approach, instead of being a few pennies would be several hundred dollars! This latter approach would also take significantly more time.
You may want to upload your own data to BigQuery or to store results of your queries as new BigQuery tables. In BigQuery, storage costs are based on the amount of data stored. For example, ISB-CGC is hosting PanCancer Atlas tables in BigQuery and is paying for the storage costs (with support from NCI). The size of each PanCancer Atlas table is less than 1.5 GB and therefore costs less than $0.25 per year to store.
For more information, see the following Google support pages: