How do you claim a child as a dependent but take the child tax credit for that child?

It cannot be done ... the person claiming the child as a dependent  gets the CTC period.

There is no such thing in the Federal tax law as 50/50, split, or joint custody.  The IRS only recognizes physical custody (which parent the child lived with the greater part, but over half, of the tax year.  That parent is the custodial parent; the other parent is the noncustodial parent.)

Who can claim the exemption and credits depends on who is the custodial parent. (By the IRS definition of custodial parent for tax purposes - this is not the same as the legal custody that a court might grant.).

The test that the IRS uses to determine the custodial parent is where the child lived for more than 1/2 (or greater part) of the year. The IRS will go so far as to require counting the nights spend in each household - that person is the custodial parent for tax purposes (if exactly equal and more than 183 days - The custodial parent is the parent with the highest AGI, if less than 183 days then neither parent has custody so the child cannot be claimed by either parent). And yes they are that picky.

See Custodial parent and noncustodial parent  under the residency test in Pub 17

https://www.irs.gov/publications/p17#en_US_2017_publink1000170899
 
Only the Custodial parent can claim: (Child would be listed as non-dependent EIC & CC only)
-Head of Household 
-Earned Income Credit
-Child Care Credit

The non custodial parent can only claim: (Child would be listed as dependent)
-The Exemption
-The Child Tax Credit

But only if specifically specified in a pre-2009 divorce decree, separation agreement or the custodial spouse releases the exemption with a signed 8332 form - after 2009 the IRS only accepts a signed 8332 form that must be attached to the non-custodial parents tax return.

Note. If you are the non-custodial parent filing your return electronically, you must file Form 8332 with Form 8453, (U.S. Individual Income Tax Transmittal) for an IRS e-file Return. See Form 8453 and its instructions for more details.  This must be done within 3 days of your e-filed return being accepted by the IRS.

Are you the custodial parent?   Do you have a signed form 8332 to allow the other parent to get the child tax credit?   If so, then when you enter your child's information in My Info you say that you have a signed agreement with the other parent.   That way, you get the childcare credit, earned income credit, and head of household filing status, but the other parent can get the child tax credit.

What are you trying to accomplish? And what is your living situation vis a vis the other parent?

  If you and the other parent are not married and live together (or are married and filing separate returns), either one of you (but not both) may claim the child. You may not split the tax attributes. You may decide between you which one will claim the child. Only if you can’t agree, do the IRS tie breaker rules apply, to see who has first choice. It may be worthwhile to prepare trial returns, both ways,  to see which way the family comes out best. This tool may be useful: https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1.

On the other hand, if you are the custodial parent, and are allowing the non custodial parent to claim the child this year, you should be aware that there is a special rule in the case of divorced & separated (including never married) parents. When the non-custodial parent is claiming the child as a dependent/child tax credit; the custodial parent is still allowed to claim the same child for Earned Income Credit, Head of Household filing status, and day care credit. This "splitting of the child" is not available to parents who lived together at any time during the last 6 months of the year; then only one of you can claim the child for any tax reasons. The tax benefits may not be split in any other manner.

Note in particular that the non-custodial parent can never claim the Earned Income Credit, Head of Household filing status or the day care credit, based on that child, even when the custodial parent has released the dependency to him.